##### On the Estimation of Stress Strength Reliability Parameter of Weibull-Rayleigh Distribution

Eno E. E. Akarawak, Matthew Iwada Ekum, Sheriffdeen Taiwo Oyeyemi

Asian Journal of Probability and Statistics, Page 1-21
DOI: 10.9734/ajpas/2022/v19i430473

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.

##### Improved Estimators of Population Coefficient of Variation under Simple Random Sampling

Rajesh Singh, Anamika Kumari

Asian Journal of Probability and Statistics, Page 22-36
DOI: 10.9734/ajpas/2022/v19i430474

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.

##### Effect of Entry Requirement and Secondary School Type on Cumulative Grade Point Average of Students in Taraba State University, Nigeria

I. Abdulmudallib, D. Jibasen, O. A. Bamigbala

Asian Journal of Probability and Statistics, Page 37-45
DOI: 10.9734/ajpas/2022/v19i430475

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.

##### Data Analysis and Modelingof Claim Amounts of Car Insurance using Big Data: A Study for Pakistan

S. M. Aqil Burney, Laiq Muhammad Khan, Shumaila Burney, Muhammad Humayoun

Asian Journal of Probability and Statistics, Page 46-53
DOI: 10.9734/ajpas/2022/v19i430476

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.

##### Generalized Moment Generating Functions for Some Continuous Multivariate Probability Distributions

Matthew Chukwuma Michael

Asian Journal of Probability and Statistics, Page 54-68
DOI: 10.9734/ajpas/2022/v19i430477

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.