Asian Journal of Probability and Statistics

Journal Information
EISSN : 2582-0230
Published by: Sciencedomain International (10.9734)
Total articles ≅ 401
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Rajesh Singh, Sat N. Gupta,
Asian Journal of Probability and Statistics pp 39-49; https://doi.org/10.9734/ajpas/2022/v20i130482

Abstract:
In this paper three efficient exponential ratio type estimators of finite population mean in the Adaptive Cluster Sampling design have been proposed using one known auxiliary variable. The expressions of bias and mean squared error of the proposed estimators are derived up to the first order of approximation. A simulation study has been conducted on two different populations to examine the performance of the proposed estimator over similar existing estimators in the Adaptive Cluster Sampling design. The simulation study showed that the proposed estimators perform better than other related estimators discussed in this article.
, Jane Akinyi, Samuel Mwalili
Asian Journal of Probability and Statistics pp 31-38; https://doi.org/10.9734/ajpas/2022/v20i130481

Abstract:
Aims/ Objectives: To determine the appropriate utility function that models the trade o between health and wealth for HIV/AIDS patients on Antiretroviral Therapy in Kenya. Study Design: Retrospective study. Place and Duration of Study: Jomo Kenyatta University of Agriculture and Technology, between January 2019-April 2022. Methodology: The study involved a retrospective study of 2800 patients on Antiretroviral Therapy in Kenya from the period of 2005-2017. All the records are in terms of random patient id and in no way is the privacy and anonymity of patients is compromised. The inclusion criteria is patients who had complete information on the covariates used in the model over the follow up period. The logarithmic utility function, the negative exponential utility function and the power utility function are compared using the Akaike Information Criterion to determine which one best fits the empirical data to model the health and wealth trade off of patients on Antiretroviral Therapy in Kenya. Results: Women constituted 66% of the sample. Only patients over the age of 18 years were included in the study. The mean age was 40.3. The health related quality of life values were calculated for each patient on Antiretroviral Therapy using the proxy utility function approach. The costs associated with receiving Antiretroviral Therapy treatment were obtained from simulating from a gamma distribution with ranges from existing published literature. The logarithmic utility function had the least AKaike Information Criterion. Conclusion: The marginal utility of health increases with wealth for People living with HIV and the logarithmic utility function is suitable for modelling the shape of preferences for the trade off between health and wealth for HIV patients on Antiretroviral Therapy.
, Okechukwu J. Obulezi
Asian Journal of Probability and Statistics pp 16-30; https://doi.org/10.9734/ajpas/2022/v20i130480

Abstract:
In this paper, a new one-parameter distribution named Chris-Jerry is suggested from two component mixture of Exponential (\(\theta\)) distribution and Gamma(3; \(\theta\)) distribution with mixing proportion \(p=\frac{\theta}{\theta + 2}\) having a flexibility advantage in modeling lifetime data. The statistical properties are discussed and the maximum likelihood estimation procedure is used to obtain the parameter estimate. The Convolution of the product of Pareto random variable with the proposed Chris-Jerry distributed random variable is explored with its marginal density derived. To illustrate the usefulness, three sets of lifetime data are employed and LL, AIC, BIC and K-S statistics are obtained for Exponential, Ishita, Akash, Rama, Pranav, Rani, Lindley, Sujatha, Aradhana, Shanker and XGamma and the Chris-Jerry distributions.
, Jane Akinyi, Samuel Mwalili
Asian Journal of Probability and Statistics pp 8-15; https://doi.org/10.9734/ajpas/2022/v20i130479

Abstract:
Aims: This study seeks to estimate QALYs for HIV/AIDS patients on ART in Kenya to quantitatively evaluate the health impact of ART treatment on patients. QALYs values are important as they form a basis for evidence based decision making and policy formulation in the country with regards to HIV/ AIDS. Study Design: The study involved secondary data obtained from a retrospective follow up study on hospital records of HIV/AIDS patients enrolled for ART from 2005 to 2017. Place and Duration of Study: Jomo Kenyatta University of Agriculture and Technology, between January 2019-April 2022. Methodology: The study involved a retrospective study of 3000 patients on ART in Kenya from the period of 2005-2017. All the patient records are identified using random patient id ensuring the privacy and anonymity of patients. The inclusion criteria is patients who had complete information on the covariates used in the model during follow up. The joint modelling of the longitudinal and survival data of each patient was applied and the results applied to proxy utility function to estimate the QALYs for patients on ART. To get the average QALYs gained by all patients, we aggregate the total QALYs from each patient. R. Software version 4.0.2 was used in the analysis. Results: Sex, age, Marital Status and weight are significant predictors of survival of HIV Patients on ART in Kenya. Being on ART therapy resulted in a gain of 9.688313 QALYs for HIV/AIDS patients. The association parameter estimate is-0.0345 implying that increase in the values of CD4 count results in a decrease in the hazard of death for HIV patients on ART therapy. Conclusion: The proxy utility function methodology is appropriate for the calculation of QALYs values for HIV patients on ART. It has the advantage of allowing utilities of each patient to vary and are calculated at every time point. Since ART results in the improvement in QALYs of patients, efforts should be directed towards ensuring patients who are enrolled for the therapy continue with it for sustained health and non health benefits.
, Emem Ndah Happiness Inamete, Makuachukwu James-Patrick Onyekwuluje
Asian Journal of Probability and Statistics pp 1-7; https://doi.org/10.9734/ajpas/2022/v20i130478

Abstract:
This paper studied the applications of genetic distances on Blood-group gene frequencies and their Statistical genetic similarities characterizing four populations, for data from Eakimo, Bantu, English and Korea. The study compared the following distances: Euclidean, squared Euclidean, Minkowski, Chebychev and City Block on the above mentioned data for the outlined countries. Correlation analysis was applied to evaluate the relationships between these countries on their blood group gene frequencies. Similarity check was also conducted to know the countries that have similar blood-group gene frequency. It was observed that Euclidean distance and Minkowski distance had equal distances. This means that the two distances are more similar in this particular data set than the other studied distances. The study revealed that Chebychev distance had the smallest neighbor distance as compared to other distances studied while City Block had the highest distance. It has been stated in literature that Chebychev and Minkowski distances are concentric circle shape, this suggests the reason behind their equality of distance. It is therefore proposed that the data may be a concentric circle data.
Matthew Chukwuma Michael
Asian Journal of Probability and Statistics pp 54-68; https://doi.org/10.9734/ajpas/2022/v19i430477

Abstract:
The traditional moment generating functions of random variables and their probability distributions are known to not exist for all distributions and/or at all points and, where they exist, serious difficult and tedious manipulations are needed for the evaluation of higher central and non-central moments. This paper developed the generalized multivariate moment generating function for some random vectors/matrices and their probability distribution functions with the intention to replace the traditional/conventional moment generating functions due to their simplicity and versatility. The new functions were developed for the multivariate gamma family of distributions, the multivariate normal and the dirrichlet distributions as a binomial expansion of the expected value of an exponent of a random vector/matrix about an arbitrarily chosen constant. The functions were used to generate moments of random vectors/matrices and their probability distribution functions and the results obtained were compared with those from existing traditional/conventional methods. It was observed that the functions generated same results as the traditional/conventional methods; in addition, they generated both central and non-central moments in the same simple way without requiring further tedious manipulations; they gave more information about the distributions, for instance while the traditional method gives skewness and kurtosis values of and respectively for -variate multivariate normal distribution, the new methods gives ((0))p*1 and respectively and; they could generate moments of integral and real powers of random vectors/matrices.
, Laiq Muhammad Khan, Muhammad Humayoun
Asian Journal of Probability and Statistics pp 46-53; https://doi.org/10.9734/ajpas/2022/v19i430476

Abstract:
Modelling of data of claim amount is of paramount importance to manage risk reserve for payment of claims. Actuaries model uncertainty using probability distributions. In this research paper claim amount distribution of the data of an insurance concern has been estimated and analysis was performed on big-data of claim amounts for better understanding and fitting of various probability distribution using R. It was noticed that the claim amounts distribution is highly positive skewed, therefore we have studied Exponential distribution, Gamma distribution and Weibull distribution as possible candidates for modelling the claim amount data. Chi Square test has been used as goodness of fit technique to decide suitable statistical model to representing the claim amounts under study. Exponential distribution is found suitable for modelling the data under study. Proposed model is usefulto estimate claim amount on aggregate for insurance concern when total loss is required to be computed to manage the risk reserve for the payments of claims.
, D. Jibasen, O. A. Bamigbala
Asian Journal of Probability and Statistics pp 37-45; https://doi.org/10.9734/ajpas/2022/v19i430475

Abstract:
This paper considered the effect of student's entry requirements, Secondary school type and Cumulative Grade Point Average of the 2014/2015 final year students of the four faculties of the Taraba State University. Primary data was collected through the use of a questionnaire from the respondents of the selected programmes from each faculty. Correlation Analysis was carried out on the students', CGPA's at lower levels, UTME score, SSCE results and Secondary school type. It was discovered that only CGPA at the end of 300 level has significant relationship with CGPA at the current level while the stepwise regression analysis shows that only CGPA at 300 level is the best predictors of students' graduation CGPA all other variables are not significant and regression analysis was used to established models for predicting graduation CGPA. Based on the findings of the study, it can therefore be concluded that entry requirements have no effect in determining the performance of students while at the university. That only CGPA at 300 level has an effect in determining students’ performance. The study therefore recommends, among others, that since UTME scores are poor predictors of student academic performance, Taraba State University should be conducting a POST-UTME examination before giving admissions to students.
Eno E. E. Akarawak, Matthew Iwada Ekum, Sheriffdeen Taiwo Oyeyemi
Asian Journal of Probability and Statistics pp 1-21; https://doi.org/10.9734/ajpas/2022/v19i430473

Abstract:
The reliability of a component depends on the stress conditions of the operating environment, which are uncertainty and should be modeled as random. This article deals with the estimation of the stress-strength reliability parameter of Weibull-Rayleigh distribution. Let X and Y be two independent random variables, where X and Y follow Weibull-Rayleigh distribution. The maximum likelihood estimator and the approximate maximum likelihood estimator of the stress-strength reliability are obtained. Other properties of the Weibull-Rayleigh distributions are derived. Two real data applications are given for showing the flexibility of the Weibull-Rayleigh stress-strength reliability.
Rajesh Singh,
Asian Journal of Probability and Statistics pp 22-36; https://doi.org/10.9734/ajpas/2022/v19i430474

Abstract:
In this article, we suggest some novel estimators of population Coefficient of Variation (CV) of the study variable using the known information on an auxiliary variable like population mean and population variance. Up to the first order of approximation, formulas for the bias and Mean squared Errors (MSE) of the proposed estimators are obtained. The efficiencies of proposed and competing estimators are evaluated by comparing their MSEs. A real and two simulated data sets are used to verify the efficiency conditions. The results showed that the proposed estimators were more efficient than the other existing estimators considered in the study.
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