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Results in Journal Asian Journal of Probability and Statistics: 302

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, Yusuf Zeren, Abdu Alameri
Asian Journal of Probability and Statistics pp 54-75; https://doi.org/10.9734/ajpas/2021/v15i430364

Abstract:
In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 \(\otimes\) G2, Cartesian product G1 x G2, composition G1 \(\circ\) G2, strong product G1 * G2, disjunction G1 V G2 and symmetric difference G1 \(\oplus\) G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V PHX[q, p], V-Phenylenic Nanotorus V PHY [m, n] and Titania Nanotubes TiO2.
, Anas Musah, Frank Kofi Owusu, Isaac Afari Addo
Asian Journal of Probability and Statistics pp 38-53; https://doi.org/10.9734/ajpas/2021/v15i430362

Abstract:
Renewable Energy Resources have been identified among the most promising sources of harnessing power for industrial and household consumption but their power generations highly uctuate so building renewable power systems without critical reliability analysis might result in frequent blackouts in the power system. Therefore, in this paper, a robust, effective and ecient design approach is proposed to handle the reliability issues. The study involves a Mathematical modelling strategy of the PV system to estimate the total PV power produced and the Bottom-Up approach for predicting the household load demand. The reliability is defined in terms of Loss of Load Probability. The design methodology was validated with a University Household. The data used for the analysis consists of daily average global solar irradiance and load profiles. The results revealed that throughout the year, November-February is where the system seems to be more reliable. Also, the results indicated that without buck-up systems, the system would experience an average annual power loss of 17.8753% and thus, it is recommended that either solar batteries or the grid are used as backup system to achieve a complete level of reliability.
Olawale Basheer Akanbi
Asian Journal of Probability and Statistics pp 21-37; https://doi.org/10.9734/ajpas/2021/v15i430361

Abstract:
The relationship between government expenditure and its revenue is generating serious debate among researchers. Similarly, their has been a controversy between the classical and the bayesian modelling. Therfore, this study examined the relationship between the government expenditure and its revenue in Nigeria using the bayesian approach. The finance data extracted from the Central Bank of Nigeria statistical bulletin from 1989 to 2018 were considered for the study. Bayesian linear regression was used to fit the model. Normal distribution was fit for the likelihood. Thus, normal-gamma prior was elicited for the bayesian regression parameters. The result showed that the Bayesian estimates with elicited normal-gamma prior produced a better posterior mean of 0.536 for the Total Revenue with a smaller posterior standard deviation of 0.00001 when compared with the OLS standard deviation of 0.05256. Similarly, the total revenue explained 78% variations in the Total expenditure. The constructed model fit was: Total Expenditure = 98.57128 + 0.53630* Total Revenue. This showed that a naira unit of the total expenditure will always be increased by 0.54 of the total revenue. Forecast of 30 years for the total expenditure using both OLS and Bayesian (normal gamma prior) were increasing as the years were progressing. Government should look for a way to increase its revenue in order to sustain the future expenses of the government since expenditure increases yearly.
Nojood A. Al-Khadari, Mahiuob M. Q. Shubatah
Asian Journal of Probability and Statistics pp 10-20; https://doi.org/10.9734/ajpas/2021/v15i430360

Abstract:
Aims / Objectives: In this paper, we introduced and investigated the concept of split domination in interval-valued fuzzy graph and denoted by γs. We obtained many results related to γs. We investigated and study the relationship of γs with other known parameters in interval-valued fuzzy graph. Finally we calculated γs(G) for some standard interval valued fuzzy graphs.
, Indah Yanti, Adi Kusumaningrumi, Agus Wahyu Widodo
Asian Journal of Probability and Statistics pp 1-9; https://doi.org/10.9734/ajpas/2021/v15i430358

Abstract:
Aims: This study aims to analyze the influence of Village Government Policies, Village Financial Institutions, Resources, and Community Factors on the Success of the Establishment of Village-Owned Enterprises (VOE) with Village Government Support as moderating variables. Study Design: SEM WarpPLS. Place: Sumberputih Village, East Java, Indonesia. Methodology: This research is quantitative research. The research instrument used a questionnaire. The research was conducted in Sumberputih Village, East Java, Indonesia. The sampling process used a simple random sampling technique and obtained 100 respondents. Data analysis using SEM WarpPLS. Results: The results showed that the Village Government Policy, Village Financial Institutions, Resources, and Community Factors had a significant effect on the success of the establishment of VOE (Y). Meanwhile, Village Government Support cannot moderate the influence of the four variables on the success of VOE establishment.
, Riyanti Isaskar, Intan Rahmawati, Lailil Muflikhah
Asian Journal of Probability and Statistics pp 58-72; https://doi.org/10.9734/ajpas/2021/v15i330359

Abstract:
Purpose: This study aims to map the level of family welfare in the Wajak District. Methods: This study uses a survey method with a mixed-method approach. The data used in this study is secondary data regarding HDI (Human Development Index), ISSI (Infrastructure Service Satisfaction Index), and EQI (Environmental Quality Index). The population in this study was all villages in Wajak District, which amounted to 13 villages. Then with the sampling technique using simple random sampling, the village selected as the sample for analysis is Bringin Village. The data analysis used in this study includes biplot, cluster, and IPA analysis. Findings: The result of this study is that the level of welfare of the community in Bringin Village is said to be quite prosperous, this can be seen from the results of mapping the variables of religiosity, entrepreneurship, and service quality showing that cluster 1 is quite prosperous with 39 members, while in cluster 2, which is less prosperous, there are 11 members. Originality: The outputs obtained for the Wajak Rural community include a mapping related to the level of family welfare and its distribution in various areas in the Wajak District area.
Zafar Iqbal, Muhammad Rashad, Iram Rauf, Muhammad Salman
Asian Journal of Probability and Statistics pp 35-57; https://doi.org/10.9734/ajpas/2021/v15i330356

Abstract:
A new BEME distribution known as beta Exponentiated moment exponential (BEME) distribution is proposed. We provide here some shape properties, moments in the form of special functions, mean deviations of BEME distribution. We derive mathematical properties of the BEME distribution including the reliability measures, the Bonferroni and the Lorenz curves, rth order statistics, measures of uncertainty: the Shannon entropy measure and the s-entropy measure. The parameters of the BEME distribution are estimated by the method of maximum likelihood estimation and estimated non-linear equations for these estimates are presented. The application of BEME distribution is explored in three different fields of engineering.
Asian Journal of Probability and Statistics pp 26-34; https://doi.org/10.9734/ajpas/2021/v15i330355

Abstract:
The arcsine distribution is very important tool in statistics literature especially in Brownian motion studies. However, modelling real data sets, even when the potential underlying distribution is pre-defined, is very complicated and difficult in statistical modelling. For this reason, we desire some flexibility on the underlying distribution. In this study, we propose a new distribution obtained by arcsine distribution with Azzalini’s skewness procedure. The main characteristics of the proposed distribution are determined both with theoretically and simulation study.
O. Michael Okoli, George A. Osuji,
Asian Journal of Probability and Statistics pp 11-25; https://doi.org/10.9734/ajpas/2021/v15i330354

Abstract:
In this paper, we present a new lifetime distribution known as the generalized inverse power Sujatha distribution. The statistical and mathematical properties of the new distribution such as the moment and moment generating function, Renyi entropy and distribution of order statistics have been derived and discussed. Also, reliability measures like survival function, hazard function, reverse hazard rate, cumulative hazard rate and odds function are discussed. Maximum likelihood estimation technique was used to estimate the parameters. However, a 95% confidence intervals were constructed for the parameters. Finally, we applied the proposed distribution to two lifetime datasets and compare its superiority over other candidate models. Results obtained indicates that the generalized inverse power Sujatha distribution outperform the other competing models.
Olawale Basheer Akanbi
Asian Journal of Probability and Statistics pp 1-10; https://doi.org/10.9734/ajpas/2021/v15i330353

Abstract:
Poverty is global serious issue which differs in various cultures across the world and over time, varies according to the understanding of the society. Poverty is the level wherein an individual or people do not have the fundamental money-related assets and basics for the least expectation for everyday comforts. Therefore, this study applies a bayesian approach to poverty rates using the wealth index data in the south-western part of Nigeria to examine their poverty levels. The likelihood was Bernoulli and the conjugate Beta distribuitions at five different parameter values [Beta (1, 1), Beta (2, 2), Beta (4, 4), Beta (8, 8) and Beta (10, 10)] were elicited for the prior. Thus, the Beta-Bernoulli posteriors were derived, fitted and their parameters estimated for both the poor data set and the non-poor data set. The result for the poor data showed that as values of the prior parameters increases the posterior mean increases and the posterior variance decreases. So, at Beta (10, 10), the posterior standard variance is the lowest which indicates that about 36% of South-Western Nigeria population are extremely poor. Also, the result for the non poor data shows that as the values of the posterior parameters increases with increase in the prior parameters values, the posterior variance for prior, Beta (1, 1) has the least value 10.78%. This means that about 11% of South-Western Nigeria population are extremely non poor (rich).
Muzamil Jallal, , Rajnee Tripathi
Asian Journal of Probability and Statistics pp 75-89; https://doi.org/10.9734/ajpas/2021/v15i230352

Abstract:
In this study a new generalisation of Rayleigh Distribution has been studied and referred it is as “A New Two-Parametric Maxwell-Rayleigh Distribution”. This distribution is obtained by adopting T-X family procedure. Several distributional properties of the formulated distribution including moments, moment generating function, Characteristics function and incomplete moments have been discussed. The expressions for ageing properties have been derived and discussed explicitly. The behaviour of the pdf and Hazard rate function has been illustrated through different graphs. The parameters are estimated through the technique of MLE. Eventually the versatility and the efficacy of the formulated distribution have been examined through real life data sets related to engineering science.
, Mojeed Abiodun Yunusa, Aminu Bello Zoramawa, Samaila Buda, Ran Vijay Kumar Singh
Asian Journal of Probability and Statistics pp 59-74; https://doi.org/10.9734/ajpas/2021/v15i230351

Abstract:
Human-assisted surveys, such as medical and social science surveys, are frequently plagued by non-response or missing observations. Several authors have devised different imputation algorithms to account for missing observations during analyses. Nonetheless, several of these imputation schemes' estimators are based on known auxiliary variable parameters that can be influenced by outliers. In this paper, we suggested new classes of exponential-ratio-type imputation method that uses parameters that are robust against outliers. Using the Taylor series expansion technique, the MSE of the class of estimators presented was derived up to first order approximation. Conditions were also specified for which the new estimators were more efficient than the other estimators studied in the study. The results of numerical examples through simulations revealed that the suggested class of estimators is more efficient.
Ekaette Inyang Enang, , T. T. Ojewale
Asian Journal of Probability and Statistics pp 41-58; https://doi.org/10.9734/ajpas/2021/v15i230350

Abstract:
This study employed the method of calibration on product type estimator to propose calibration product type estimators using three distance measures namely; chi-square distance measure, the minimum entropy distance measure and the modified chi-square distance measure for single constraint. The estimators of variances of the proposed estimators were also obtained. An empirical study to ascertain the performance of these estimators was carried out using real life and stimulated data set. The result with the real life data showed that the proposed calibration product type estimator produced better estimates of the population mean compared to and . Results from the simulation study showed that the proposed calibration product type estimators had a high gain in efficiency as compared to the product type estimator. The simulation result also showed that the proposed estimators were more consistent and reliable under the Gamma and Exponential distributions with the exponential distribution taking the lead. The conventional product type estimator however was found to be better if the underlying distributional assumption is normal in nature.
, Lewis Brew, Suleman Nasiru
Asian Journal of Probability and Statistics pp 18-40; https://doi.org/10.9734/ajpas/2021/v15i230349

Abstract:
In this paper, we propose a three-parameter probability distribution called equilibrium renewal Burr XII distribution using the equilibrium renewal process. The statistical properties of the distribution such as moment, mean deviation, order statistics, moment generating function, Beforroni and Lorenz curve, survival function, reversed hazard rate and hazard function were derived. The method of maximum likelihood is used for estimating the distribution's parameters and a simulation study is conducted to assess the performance of the parameters. We provide two applications in eld of health to demonstrate the importance of the proposed distribution.
, Okoli Juliana Ifeyinwa, Haruna Umar Yahaya
Asian Journal of Probability and Statistics pp 1-17; https://doi.org/10.9734/ajpas/2021/v15i230348

Abstract:
Assumptions in the classical linear regression model include that of lack of autocorrelation of the error terms and the zero covariance between the explanatory variable and the error terms. This study is channeled towards the estimation of the parameters of the linear models for both time series and cross-sectional data when the above two assumptions are violated. The study used the Monte-Carlo simulation method to investigate the performance of six estimators: ordinary least square (OLS), Prais-Winsten (PW), Cochrane-Orcutt (CC), Maximum Likelihood (MLE), Restricted Maximum- Likelihood (RMLE) and the Weighted Least Square (WLS) in estimating the parameters of a single linear model in which the explanatory variable is also correlated with the autoregressive error terms. Using the models’ finite properties(mean square error) to measure the estimators’ performance, the results shows that OLS should be preferred when autocorrelation level is relatively mild (ρ = 0.3) and the PW, CC, RMLE, and MLE estimator will perform better with the presence of any level of AR (1) disturbance between 0.4 to 0.8 level, while WLS shows better performance at 0.9 level of autocorrelation and above. The study thus recommended the application of the various estimators considered to real-life data to affirm the results of this simulation study.
Iwok Iberedem Aniefiok, Barinaadaa John Nwikpe
Asian Journal of Probability and Statistics pp 35-45; https://doi.org/10.9734/ajpas/2021/v15i130347

Abstract:
In this paper, a new continuous probability distribution named Iwok-Nwikpe distribution is proposed. Some essential statistical properties of the proposed probability distribution have been derived. The graphs of the survival function, probability density function (p.d.f) and cumulative distribution function (c.d.f) were plotted at different values of the parameter. The mathematical expression for the moment generating function (mgf) was derived. Consequently, the first three crude moments were obtained; the distribution of order statistics, the second and third moments corrected for the mean have also been derived. The parameter of the Iwok-Nwikpe distribution was estimated by means of maximum likelihood technique. To establish the goodness of fit of the Iwok-Nwikpe distribution, three real data sets from engineering and medical science were fitted to the distribution. Findings of the study revealed that the Iwok-Nwikpe distribution performed better than the one parameter exponential distribution and other competing models used for the study.
Asian Journal of Probability and Statistics pp 30-34; https://doi.org/10.9734/ajpas/2021/v15i130346

Abstract:
Sometimes, outcomes of random processes don’t seem to follow the theoretical probabilities due to the presence of bias and even when the probabilities are followed in a large number of trials, dynamic bias is still evident in many of these processes. This paper provides a short study on the bias using examples and defines what kind of processes could be biased. It also demonstrates the two types of bias which are dynamic and fixed. This study could be used to analyze the bias in various random processes and get a better understanding of the outcomes. Dynamic bias has further been explained with the help of 52 cards. The study helps in providing a better understanding of randomness and further helps in designing experiments.
Asian Journal of Probability and Statistics pp 15-29; https://doi.org/10.9734/ajpas/2021/v15i130345

Abstract:
Based on the Weibull-G Power probability distribution family, we have proposed a new family of probability distributions, named by us the Max Weibull-G power series distributions, which may be applied in order to solve some reliability problems. This implies the fact that the Max Weibull-G power series is the distribution of a random variable max (X1 ,X2 ,...XN) where X1 ,X2 ,... are Weibull-G distributed independent random variables and N is a natural random variable the distribution of which belongs to the family of power series distribution. The main characteristics and properties of this distribution are analyzed.
Ismaila A. Bolarinwa, Bushirat T. Bolarinwa
Asian Journal of Probability and Statistics pp 8-14; https://doi.org/10.9734/ajpas/2021/v15i130344

Abstract:
The order of bias of the fixed effects gompertz model is studied, using Monte Carlo approach. Performance criteria are bias and root mean squared errors. For fixed N, bias is found to decrease steadily between T=5 and T=20 but exhibits a mixture of increase and decline afterwards. At each value of T involved, bias steadily decreases with increased value of N. Bias is found to be at most 123%, due to the combination of minimum of each of N and T involved. Decrease in order of bias is found to be more definite with increased N at fixed T than with increased T at fixed N.
A. B. Zoramawa, S. U. Gulumbe
Asian Journal of Probability and Statistics pp 1-7; https://doi.org/10.9734/ajpas/2021/v15i130339

Abstract:
This paper proposed a sequential probability sampling plan for a truncated life test using a Rayleigh distribution from a designed double sampling plans where the interest was to obtain the minimum sample size necessary to assure that the average life time of a product is longer than the default life time at the specified consumer’s and producer’s confidence level. Estimations of minimum sample, acceptance and rejection numbers obtained are analyzed and presented to explain the usefulness of sequential plans in relation to single and double sampling plan. Probability of acceptance (Pa), Average sample number (ASN) and Average outgoing quality (AOQ) for the plans are computed. The three regions; acceptance, continue sampling and rejection were determined. The five points necessary to plot ASN curve were also computed and presented.
A. Y. Erinola, R. V. K. Singh, A. Audu, T. James
Asian Journal of Probability and Statistics pp 52-64; https://doi.org/10.9734/ajpas/2021/v14i430338

Abstract:
This study proposed modified a class of estimator in simple random sampling for the estimation of population mean of the study variable using as axillary information. The biases and MSE of suggested estimators were derived up to the first order approximation using Taylor’s series expansion approach. Theoretically, the suggested estimators were compared with the existing estimators in the literature. The mean square errors (MSE) and percentage relative efficiency (PRE) of proposed estimators and that of some existing estimators were computed numerically and the results revealed that the members of the proposed class of estimator were more efficient compared to their counterparts and can produce better estimates than other estimators considered in the study.
Brijesh P. Singh, Sandeep Singh,
Asian Journal of Probability and Statistics pp 41-51; https://doi.org/10.9734/ajpas/2021/v14i430337

Abstract:
Migration is a term that encompasses a permanent or temporary change in residence between some specific defined geographical or political areas. In recent years, it has not only contributed a lot to the change in size and composition of the population, but also it leaves a significant impact on the socio-economic characteristics of the origin and destination population. In the present paper an attempt has been made to examine the distribution of the number of rural out migrants from household through composite probability models based on certain assumptions. Poisson distribution compounded with exponential distribution and its composite and in ated form has been examined for some real data set of rural out migration. The parameters of the proposed models have been estimated by method of moments. The distributions are quite satisfactory to explain the phenomenon of rural out migration. Also the distribution of average number of adult migrants has been examined for all the data sets.
, A. Abdulkadir, H. Chiroma, U. F. Abbas
Asian Journal of Probability and Statistics pp 21-40; https://doi.org/10.9734/ajpas/2021/v14i430336

Abstract:
In this article a new generalization of the skew student-t distribution was introduced. The two-parameter model called the type I half-logistic skew-t (TIHLST) distribution can fit skewed, heavy-right tail, and long-tail datasets. Statistical properties of the type I half-logistic skew-t (TIHLST) distribution were derived and the maximum likelihood method parameter estimates assessed through a simulation study. A well-known dataset was analysed, illustrating the usefulness of the new distribution in modeling skewed and heavy-tailed data. The hazard rate shape was found to be increasing, decreasing and inverted bathtub shaped which was also reflected in the application result.
A. Adetunji Ademola, Shamsul Rijal Muhammad Sabri
Asian Journal of Probability and Statistics pp 14-20; https://doi.org/10.9734/ajpas/2021/v14i430334

Abstract:
Background: In modelling claim frequency in actuary science, a major challenge is the number of zero claims associated with datasets. Aim: This study compares six count regression models on motorcycle insurance data. Methodology: The Akaike Information Criteria (AIC) and the Bayesian Information Criterion (BIC) were used for selecting best models. Results: Result of analysis showed that the Zero-Inflated Poisson (ZIP) with no regressors for the zero component gives the best predictive ability for the data with the least BIC while the classical Negative Binomial model gives the best result for explanatory purpose with the least AIC.
Asian Journal of Probability and Statistics pp 1-13; https://doi.org/10.9734/ajpas/2021/v14i430333

Abstract:
This study investigates the impact of violation of the assumption of the hierarchical linear model where covariate of level – 1 collinear with the correct functional and omitted variable model. This was carried out via Monte Carlo simulation. In an attempt to achieve this omitted variable bias was introduced. The study considers the multicollinearity effects when the models are in the correct form and when they are not in the correct form. Also, multicollinearity test was carried out on the data set to find out whether there is presence of multicollinearity among the data set using Variance Inflation Factor (VIF). At the end of the study, the result shows that, omitted variable has tremendous impact on hierarchical linear model.
Alok Kumar Singh, Rohit Patawa, Abhinav Singh, Puneet Kumar Gupta
Asian Journal of Probability and Statistics pp 48-59; https://doi.org/10.9734/ajpas/2021/v14i330332

Abstract:
For a Modified Maximum Likelihood Estimate of the parameters of generalized exponential distribution (GE), a hyperbolic approximation is used instead of linear approximation for a function which appears in the Maximum Likelihood equation. This estimate is shown to perform better, in accuracy and simplicity of calculation, than the one based on linear approximation for the same function. Numerical computation for random samples of different sizes from generalized exponential distribution (GE), using type II censoring is done and is shown to be better than that obtained by Lee et al. [1].
P. K. Tripathy,
Asian Journal of Probability and Statistics pp 34-47; https://doi.org/10.9734/ajpas/2021/v14i330331

Abstract:
The purpose of the current paper is to determine an optimal order quantity so as to minimize the total cost of the inventory system of a business enterprise. The model is developed for deteriorating items with stock and selling price dependent demand under inflation without permitting shortage. Optimal solution is achieved by cost minimization strategy considering replenishment cost, purchase cost, holding cost and deterioration cost with a special approach to entropy cost for bulk size purchasing units. The effectiveness of the proposed model has been avowed through empirical investigation. Sensitivity analysis has been accomplished to deduce managerial insights. Findings suggest that an increased inflationary effect results in increment in the system total cost. The paper can be extended by allowing shortage. The model can be utilized in the business firms dealing with bulk purchasing units of electric equipments, semiconductor devices, photographic films and many more.
, Adenomon Monday Osagie
Asian Journal of Probability and Statistics pp 22-33; https://doi.org/10.9734/ajpas/2021/v14i330330

Abstract:
In a classical multiple linear regression analysis, multicollinearity and autocorrelation are two main basic assumption violation problems. When multicollinearity exists, biased estimation techniques such as Maximum Likelihood, Restricted Maximum Likelihood and most recent the K-L estimator by Kibria and Lukman [1] are preferable to Ordinary Least Square. On the other hand, when autocorrelation exist in the data, robust estimators like Cochran Orcutt and Prais-Winsten [2] estimators are preferred. To handle these two problems jointly, the study combines the K-L with the Prais-Winsten’s two-stage estimator producing the Two-Stage K-L estimator proposed by Zubair & Adenomon [3]. The Mean Square Error (MSE) and Root Mean Square Error (RMSE) criterion was used to compare the performance of the estimators. Application of the estimators to two (2) real life data set with multicollinearity and autocorrelation problems reveals that the Two Stage K-L estimator is generally the most efficient.
, Elphas Luchemo, Ayubu Anapapa
Asian Journal of Probability and Statistics pp 8-21; https://doi.org/10.9734/ajpas/2021/v14i330328

Abstract:
Malaria is one of the leading causes of deaths in Kenya. Malaria is a vector-borne disease caused by a parasite of the genus plasmodium. Complete eradication of malaria in the country has remained a problem. A lot of effort and resources has been put in the fight against malaria in developing countries which has led to underdevelopment and low human development index. Malaria burden affects the world’s poorest countries. About 90% of the malaria burden is reported in sub-Saharan Africa. The disease has led to high mortality cases in children and pregnant women. Despite the massive government eradication campaign, new and resurgent cases have been recorded. The specific objective was to determine the malaria risk factors and spatial distribution in Kenya. The 2015 malaria indicator survey data was used for the study. Demographic and social-economic factors were used as predictor variables. A generalized linear mixed model was used to determine the spatial variation and prevalence of malaria in Kenya. Demographic and social-economic factors were found to have significant impact on Prevalence of malaria in kenya. Most cases of malaria were reported in lake, western and coastal regions. The most prone areas were Kisumu, Homabay, Kakamega and Mombasa. There were less cases in central Kenya counties like Nyeri, Tharaka-Nithi with a significant number reported in arid and semi-arid regions of Northern-Kenya counties of Garissa, Mandera, Baringo. Rural population was more susceptible to malaria compared to those in urban areas. The odds of getting (verse not getting malaria) in places of residence increases by 1.32, which is estimated to .28, CIs 95% (1.01, 1.72), and a p-value .04. Malaria prevalence varied significantly from one region to another. The study established that Spatial autocorrelation exists among regions mostly due to weather patterns, geography, cultural practices and socio-economic factors.
, Sule Omeiza Bashiru, Alhaji Modu Isa, Yunusa Adavi Ojirobe
Asian Journal of Probability and Statistics pp 41-59; https://doi.org/10.9734/ajpas/2021/v14i230325

Abstract:
Gompertz Rayleigh (GomR) distribution was introduced in an earlier study with few statistical properties derived and parameters estimated using only the most common traditional method, Maximum Likelihood Estimation (MLE). This paper aimed at deriving more statistical properties of the GomR distribution, estimating the three unknown parameters via a competitive method, Maximum Product of Spacing (MPS) and evaluating goodness of fit using rainfall data sets from Nigeria, Malaysia and Argentina. Properties of statistical distributions including distribution of smallest and largest order statistics, cumulative or integrated hazard function, odds function, rth non-central moments, moment generating function, mean, variance and entropy measures for GomR distribution were explicitly derived. The fitted data sets reveal the flexibility of GomR distribution over other distributions been compared with. Simulation study was used to evaluate the consistency, accuracy and unbiasedness of the GomR distribution parameter estimates obtained from the method of MPS. The study found that GomR distribution could not provide a better fit for Argentine rainfall data but it was the best distribution for the rainfall data sets from Nigeria and Malaysia in comparison with the distributions; Generalized Weibull Rayleigh (GWR), Exponentiated Weibull Rayleigh (EWR), Type (II) Topp Leone Generalized Inverse Rayleigh (TIITLGIR), Kumarawamy Exponential Inverse Raylrigh (KEIR), Negative Binomial Marshall-Olkin Rayleigh (NBMOR) and Exponentiated Weibull (EW). Furthermore, the estimates from MPSE were consistent as the sample size increases but not as efficient as those from MLE.
E. E. Bassey, U. P. Akra
Asian Journal of Probability and Statistics pp 1-7; https://doi.org/10.9734/ajpas/2021/v14i330327

Abstract:
This research is on canonical correlation of multivariate regression analysis on economic factors in Nigeria. This study aim to analyze the effect of Nigerian macroeconomic factors and also to investigate the relationship between the factors for the period of 1985-2014. Four macroeconomic variables (economic factors) used in this research are Gross Domestic Product (GDP), Currency in Circulation (CIC), Foreign Trade and Inflation. Canonical correlation analysis under Multivariate regression was used for association between the variables. The result showed that there is a significant relationship between GDP and all the variables considered at (0.01) level of significant with the exception of inflation which showed negative and no significant relationship. However, the results also revealed that the economy of Nigeria is been affected by volume of economic factor returns.
, N. O. Nweze
Asian Journal of Probability and Statistics pp 60-73; https://doi.org/10.9734/ajpas/2021/v14i230326

Abstract:
Time series of count with over-dispersion is the reality often encountered in many biomedical and public health applications. Statistical modelling of this type of series has been a great challenge. Rottenly, the Poisson and negative binomial distributions have been widely used in practice for discrete count time series data, their forms are too simplistic to accommodate features such as over-dispersion. Unable to account for these associated features while analyzing such data may result in incorrect and sometimes misleading inferences as well as detection of spurious associations. Therefore, the need for further investigation of count time series models suitable to fit count time series with over-dispersion of different level. The study therefore proposed a best model that can fit and forecast time series count data with different levels of over-dispersion and sample sizes Simulation studies were conducted using R statistical package, to investigate the performances of Autoregressiove Conditional Poisson (ACP) and Poisson Autoregressive (PAR) models. The predictive ability of the models were observed at different steps ahead. The relative performance of the models were examined using Akaike Information criteria (AIC) and Hannan-Quinn Information Criteria (HQIC). Conclusively, the best model to fit was ACP at different sample sizes. The predictive abilities of the four fitted models increased as sample size and number of steps ahead were increased
, Etuk Ette Harrison, Isaac D. Essi
Asian Journal of Probability and Statistics pp 23-40; https://doi.org/10.9734/ajpas/2021/v14i230324

Abstract:
Aims: The aim of this study is to examine multivariate GARCH modeling of selected Nigerian economic data. Study Design: The study used monthly data of Nigerian crude oil prices (dollar Per Barrel), consumer price Index rural, maximum lending rate and prime lending rate. Methodology: This work covers time series data on crude oil prices, consumer price Index rural, maximum lending rate and prime lending rate extracted from Central Bank of Nigeria (CBN) from 2000 to 2019. In attempt to achieve the aim of the study, quadrivariate VECH and DCC model were applied. Results: The results confirmed that returns on economic data were correlated. Also, diagonal multivariate VECH model confirmed one of the properties that it must be ‘positive semi-definite’, And the DCC confirmed also the positive-definite conditional-variance. Conclusion: From the results obtained, it was confirmed that there exists a strong confirmation of a time-varying conditional covariance and interdependence among Nigeria economic data. As for cross-volatility effects, past innovations in crude oil price have utmost control on future volatility of returns on economic data. It was also confirmed that time varying covariance displays among these economic data and lower degree of persistence and based on Model selection criteria using the Akaike information criteria (AIC) has 17.485 for diagonal VECH while for DCC has 17.509 AIC which makes VECH model better fitted.
M. A. Yunusa, A. Audu, N. Musa, D. O. Beki, A. Rashida, A. B. Bello, M. U. Hairullahi
Asian Journal of Probability and Statistics pp 13-22; https://doi.org/10.9734/ajpas/2021/v14i230323

Abstract:
The estimation of population coefficient of variation is one of the challenging aspects in sampling survey techniques for the past decades and much effort has been employed to develop estimators to produce its efficient estimate. In this paper, we proposed logarithmic ratio type estimator for the estimating population coefficient of variation using logarithm transformation on the both population and sample variances of the auxiliary character. The expression for the mean squared error (MSE) of the proposed estimator has been derived using Taylor series first order approximation approach. Efficiency conditions of the proposed estimator over other estimators in the study has also been derived. The empirical study was conducted using two-sets of populations and the results showed that the proposed estimator is more efficient. This result implies that, the estimate of proposed estimator will be closer to the true parameter than the estimates of other estimators in the study.
Watare Asaph,
Asian Journal of Probability and Statistics pp 1-12; https://doi.org/10.9734/ajpas/2021/v14i230322

Abstract:
Recently Social Network has become one of the favorite means for a modern society to perform social interaction and exchange information via the internet. Link prediction is a common problem that has broad application in such social networks, ranging from predicting unobserved interaction to recommending related items. In this paper, we investigate link recommendations over business pages on Facebook Social Network. More specifically, given a company in thenetwork, we want to recommend potential companies to connect with. We start by introducing existing work in link recommendations and some link prediction models as our baseline. We then talk about the Graph Neural Network model SEAL to make a link recommendations in the network. Our results show that SEAL outperformed the compared baseline model while reaching above 94% Area Under Curve accuracy in link recommendations.
, Junjuan Hu
Asian Journal of Probability and Statistics pp 41-51; https://doi.org/10.9734/ajpas/2021/v14i130321

Abstract:
In this paper, the asymptotic distribution of Fourier ESTAR model (FKSS) proposed by [1], which was not given in the original paper are derived. Result shows that the asymptotic distributions are functions of brownian motion, only depends on K and free from nuisance parameters.
Asian Journal of Probability and Statistics pp 31-40; https://doi.org/10.9734/ajpas/2021/v14i130320

Abstract:
In this paper, the limiting behaviour of the Sample Autocorrelation Function(SACF) of the errors {et} of First-Order Autoregressive (AR(1)), First-Order Moving Average (MA(1)) and First Order Autoregressive First-Order Moving Average (ARMA(1,1)) stationary time series models in the presence of a large Additive Outlier(AO) is discussed. It is found that the errors which are supposed to be uncorrelated due to either white noise process or normally distributed process are not so in the presence of a large additive outlier. The SACF of the errors follows a particular pattern based on the time series model. In the case of AR(1) model, at lag 1, the contaminated errors {et} are correlated, whereas at higher lags, they are uncorrelated. But in the MA(1) and ARMA(1,1) models, the contaminated errors {et} are correlated at all the lags. Furthermore it is observed that the intensity of correlations depends on the parameters of the respective models.
Oluwaseun A. Otekunrin, Kehinde O. Alawode
Asian Journal of Probability and Statistics pp 23-30; https://doi.org/10.9734/ajpas/2021/v14i130319

Abstract:
Group Divisible PBIBDs are important combinatorial structures with diverse applications. In this paper, we provided a construction technique for Group Divisible (v-1,k,0,1) PBIBDs. This was achieved by using techniques described in literature to construct Nim addition tables of order 2n, 2≤n≤5 and (k2,b,r,k,1)Resolvable BIBDs respectively. A “block cutting” procedure was thereafter used to generate corresponding Group Divisible (v-1,k,0,1) PBIBDs from the (k2,b,r,k,1)Resolvable BIBDs. These procedures were streamlined and implemented in MATLAB. The generated designs are regular with parameters(15,15,4,4,5,3,0,1);(63,63,8,8,9,7,0,1);(255,255,16,16,17,15,0,1) and (1023,1023,32,32,33,31,0,1). The MATLAB codes written are useful for generating the blocks of the designs which can be easily adapted and utilized in other relevant studies. Also, we have been able to establish a link between the game of Nim and Group Divisible (v-1,k,0,1) PBIBDs.
Asian Journal of Probability and Statistics pp 12-22; https://doi.org/10.9734/ajpas/2021/v14i130318

Abstract:
A new sole parameter probability distribution named the Tornumonkpe distribution has been derived in this paper. The new model is a blend of gamma (2, and gamma(3 distributions. The shape of its density for different values of the parameter has been shown. The mathematical expression for the moment generating function, the first three raw moments, the second and third moments about the mean, the distribution of order statistics, coefficient of variation and coefficient of skewness has been given. The parameter of the new distribution was estimated using the method of maximum likelihood. The goodness of fit of the Tornumonkpe distribution was established by fitting the distribution to three real life data sets. Using -2lnL, Bayesian Information Criterion (BIC), and Akaike Information Criterion(AIC) as criterial for selecting the best fitting model, it was revealed that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used.
Asian Journal of Probability and Statistics pp 1-11; https://doi.org/10.9734/ajpas/2021/v14i130317

Abstract:
A new two-parameter lifetime distribution has been proposed in this study. The distribution is called Samade distribution. The model is motivated by the wide use of the lifetime models derived from the mixture of gamma and exponential distributions. Its mathematical properties which include the first four moments, variance as well as coefficient of variation, reliability function, hazard function, survival function, Renyi entropy measure and distribution of order statistics have been successfully derived. The maximum likelihood estimation of its parameters and application to real life data have been discussed. Application of this model to three real datasets shown that the proposed model yields a satisfactorily better fit than other existing lifetime distributions. The comparism of goodness-of-fits were established using -2Loglikelihood, AIC and BIC.
E. M. A. Hassan, M. M. Said
Asian Journal of Probability and Statistics pp 47-57; https://doi.org/10.9734/ajpas/2021/v13i430315

Abstract:
In this paper, a new class of life distribution is named new better than renewal used in moment generating function (NBRUmgf). A new test for exponentiality versus NBRUmgf based on moment inequalities is established. Pitman's asymptotic efficiencies, powers and critical values of the new test are calculated to assess the performance of the test. The right censored data is handled also. Finally some applications are applied to the new test.
Prinye Bethel Brown, Isaac Didi Essi
Asian Journal of Probability and Statistics pp 12-31; https://doi.org/10.9734/ajpas/2021/v13i430313

Abstract:
Communicable diseases are a major health challenge for the world. However, their negative impacts are felt most in Africa. This panel data study investigates the effect of communicable diseases and health expenditure on the economy. Gross Domestic Product (GDP) and current health expenditure are used as proxies for economic performance and health expenditure, respectively. Incidence of Tuberculosis, prevalence of Human Immunodeficiency Virus (HIV), and adults living with HIV (15 years - above) are the health indicators used in the study. Data for a period of ten years: 2007 to 2016 were collected from seven African countries in low and middle-income countries, according to World Health Organization (WHO) income groupings. Low-income countries are Gambia, Sierra Leone, and Togo, while Egypt, Ghana, Nigeria, and South Africa are middle-income countries. The three analytical panel data models; namely: Pooled Ordinary Least Squares Model (POLS), Fixed Effects Model (FEM) and Random Effects Model (REM) were used. Model selection tests were also performed, using the F Ratio Test, the Breush-Pagan Langrange Multiplier Test, and the Hausman Test, to choose the model that best describes the data. The results of the model selection tests show that the FEM is the most appropriate model for the data; therefore, the result of the FEM is used to interpret the impact of communicable diseases on the economy. First, the FEM analysis generally showed that HIV prevalence has a statistically significant negative effect on GDP, which is consistent with the existing literature. On the other hand, the incidence of tuberculosis and adults living with HIV have statistically positive effect. The result also shows that current health expenditure per capita is positively correlated with GDP, which implies that a unit increase in current health expenditure would lead to an increase of 961 units in GDP, based on the data used. Second, an additional analysis conducted in FEM to determine the effect of the variables in each country reveal that adults living with HIV and HIV prevalence have a statistically significant negative effect on economic performance. In conclusion, communicable diseases are an impediment to economic growth. The prevention and control of these diseases is a step in the right direction towards improving economic performance.
Zafar Iqbal, Muhammad Rashad, Abdur Razaq, Muhammad Salman, Afsheen Javed
Asian Journal of Probability and Statistics pp 32-46; https://doi.org/10.9734/ajpas/2021/v13i430314

Abstract:
We introduce a new class of lifetime models called the transmuted powered moment exponential distribution. More specifically, the transmuted powered moment exponential distribution covers several new distributions. Survival analysis including survival function, hazard rate function and other related measures are computed. Analytical expressions for various mathematical properties of TPMED including rth moment, quantile function, inequality measures, and parameters are estimated by using maximum likelihood estimation and order statistics are also derived. A simulation study of the proposed distribution is performed. It is discovered that the Maximum Likelihood Estimators are consistent since the bias and Mean Square Error approach to zero when the sample size increases. The usefulness of the model associated with this distribution is illustrated by two real data sets and the new model provides a better fit than the models provided in literature.
, Halim Zeghdoudi
Asian Journal of Probability and Statistics pp 1-11; https://doi.org/10.9734/ajpas/2021/v13i430312

Abstract:
This article presents the advantages of multivariate GARCH models. Multivariate GARCH models are identified as the best and flexible models in econometrics. Also, the interest of these models is to be able to examine and analyze the various relations which the various series maintain between them. In order to be able to estimate several financial series to analyze their correlations and transfers of volatility. We present an application on the relationship between the existing volatility in the oil market and the energy market, which we found that the assembly performance of the BEKK-GARCH form is better than that of other models.
Asian Journal of Probability and Statistics pp 62-88; https://doi.org/10.9734/ajpas/2021/v13i330311

Abstract:
The paper introduces several approximate maximum likelihood estimators of the parameters of the sub-fractional Chan-Karolyi-Longstaff-Sanders (CKLS) interest rate model and obtains their rates of convergence. A new algorithm inspired by Newton-Cotes formula is presented to improve the accuracy of estimation. The estimators are useful for simulation of interest rates. The proposed new algorithm could be useful for other stochastic computation. It also proposes a generalization of the CKLS interest rate model with sub-fractional Brownian motion drivers which preserves medium range memory.
Aliyu Sani Aliyu, , M. O. Adenomon
Asian Journal of Probability and Statistics pp 30-43; https://doi.org/10.9734/ajpas/2021/v13i330310

Abstract:
Application of SARIMA model in modelling and forecasting monthly rainfall in Nigeria was considered in this study. The study utilizes the Nigerian monthly rainfall data between 1980-2015 obtained from World Bank Climate Portal. The Box-Jenkin’s methodology was adopted. SARIMA (2,0,1) (2,1,1) [12] was the best model among others that fit the Nigerian rainfall data (1980-2015) with maximum p-value from Box-Pierce Residuals Test. The study forecasts Nigeria’s monthly rainfall from 2018 through 2042. It was discovered that the month of April is the period of onset of rainfall in Nigeria and November is the period of retreat. Based on the findings, Nigeria will experience approximately equal amount of rainfall between 2018 to 2021 and will experience a slight increase in rainfall amount in 2022 to about 1137.078 (mm). There will be a decline of rainfall at 2023 to about 1061 (mm). Rainfall values will raise again to about 1142.756 (mm) in 2024 and continue to fluctuate with decrease in variation between 2024 to 2042, then remain steady to 2046 at approximately 1110.0 (mm). Nigerian Government should provide a more mechanized and drier season farming methods to ease the outage of rainfall in future that may be caused due to natural (or unpredictable) variation.
Imliyangba, , Seema Chettri
Asian Journal of Probability and Statistics pp 44-61; https://doi.org/10.9734/ajpas/2021/v13i330309

Abstract:
Generalizing probability distributions is a very common practice in the theory of statistics. Researchers have proposed several generalized classes of distributions which are very flexible and convenient to study various statistical properties of the distribution and its ability to fit the real-life data. Several methods are available in the literature to generalize new family of distributions. The Quadratic Rank Transmutation Map (QRTM) is a tool for the construction of new families of non-Gaussian distributions and to modulate a given base distribution for modifying the moments like the skewness and kurtosis with the ability to explore its tail properties and improve the adequacy of the distribution. Recently, a new family of transmutation map, defined as Cubic Rank Transmutation (CRT) has been used by several authors to develop new distributions with application to real-life data. In this article, we have done a review work on the existing generalized rank mapped transmuted probability distributions, available in the literature with various statistical properties such as the reliability, hazard rate and cumulative hazard functions, moments, mean, variance, moment-generating function, order statistics, generalized entropy and quantile function along with its applications. Some future works have also been discussed for generalized rank mapped transmuted distributions.
A. Audu, M. A. Yunusa, , M. K. Lawal, A. Rashida, A. H. Muhammad, A. B. Bello, M. U. Hairullahi, J. O. Muili
Asian Journal of Probability and Statistics pp 13-29; https://doi.org/10.9734/ajpas/2021/v13i330308

Abstract:
In this paper, three difference-cum-ratio estimators for estimating finite population coefficient of variation of the study variable using known population mean, population variance and population coefficient of variation of auxiliary variable were suggested. The biases and mean square errors (MSEs) of the proposed estimators were obtained. The relative performance of the proposed estimators with respect to that of some existing estimators were assessed using two populations’ information. The results showed that the proposed estimators were more efficient than the usual unbiased, ratio type, exponential ratio-type, difference-type and other existing estimators considered in the study.
Seema Chettri,
Asian Journal of Probability and Statistics pp 1-12; https://doi.org/10.9734/ajpas/2021/v13i330307

Abstract:
In this article a brief summary of some recent developments of Weibull lifetime models has been presented for a quick overview. Various extensions of the Weibull models and the properties of the extended Weibull distribution have been discussed. A brief discussion about the characteristics and shape behaviour has been presented in the tabular form. Finally, some future research topics have been given.
Asian Journal of Probability and Statistics pp 48-55; https://doi.org/10.9734/ajpas/2021/v13i230305

Abstract:
In this work, we describe a Bayesian procedure for detection of change-point when we have an unknown change point in regression model. Bayesian approach with posterior inference for change points was provided to know the particular change point that is optimal while Gibbs sampler was used to estimate the parameters of the change point model. The simulation experiments show that all the posterior means are quite close to their true parameter values. The performance of this method is recommended for multiple change points.
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