Asian Journal of Probability and Statistics

Journal Information
EISSN : 2582-0230
Published by: Sciencedomain International (10.9734)
Total articles ≅ 288
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, 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.
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