##### Unit Half Logistic Normal Distribution: Properties and Applications

Abdul-Aziz Adam Kobilla, Suleman Nasiru

Asian Journal of Probability and Statistics, Page 1-21
DOI: 10.9734/ajpas/2022/v18i430452

In this study, a new generalization of the normal distribution called the unit half logistic normal (UHLN) distribution has been proposed by introducing a shape parameter into the normal distribution to make it more flexible. Several statistical properties of the new distribution which include; the cumulative hazard function, reversed hazard function, hazard rate average function, quantile function, moments, moment generating function and order statistics has been derived. Estimators such as the maximum likelihood, ordinary least squares, weighted least squares and Cramér-von Mises were developed for the new model. The performances of the estimators were investigated via Monte Carlo simulation using six different sample sizes and replicated 5000 times. The maximum likelihood was observed to be the most consistent and the best technique, hence was used to estimate the parameters of the new distribution. The applications of the UHLN distribution was demonstrated using three different datasets and compared with the normal, transmuted normal, beta normal, McDonal normal and logistic distributions. The results revealed that the UHLN distribution performs better for the given datasets.

##### Walking Mathematics Students through the Maze of Chi-square Test of Independence and Homogeneity, Test Involving Several Proportions, and Goodness-of-fit Test

Charles Kojo Assuah, Thomas Mensah‒Wonkyi, Matilda Sarpong Adusei, Stephen Ghunney

Asian Journal of Probability and Statistics, Page 22-35
DOI: 10.9734/ajpas/2022/v18i430454

This study illustrates some practical steps lecturers could use to enable students to apply the chi-square concept. The study relied on a definition and theorem based on the chi-square theoretical model. The participants consisted of seventy (70) (fifty-five (55) males and fifteen (15) females) level 100 mathematics students from a university in Ghana. They were all admitted from the public senior high schools across the country. The students completed the tasks assigned to them in their various groups through active learning, as their lecturer facilitated the process. The lecturer guided the students to complete tasks related to the applications of the chi-square test in solving problems. The results indicated that active learning exposed the students to varied ways to apply the chi-square test. An implication of this study is that lecturers should teach their students about theorems and their related proofs and applications. These theorems are significant in mathematics learning because they are absolute truths. They enable students to develop a deeper understanding of the underlying concepts. The study concludes that by working with concrete examples, students gradually internalized their concept-acquisition skills to the extent that they confidently identified what concept to apply to every question.

##### On the Nonparametric Approach to Estimation of Non- Constant Variance Function: An Application to Nairobi Securities Exchange (NSE)

Peter Mwangi

Asian Journal of Probability and Statistics, Page 36-45
DOI: 10.9734/ajpas/2022/v18i430455

Methods for estimating regression models to data in the areas showing varying variances is considered. The centre of attention is on diverse methods of evaluating varying variances. The nonparametric approach which incorporates the smoothing methods and the choice of the ideal bandwidth is discussed. Normally, the cardinal shortcoming which is of interest is the selection of the smoothing method and picking of the best bandwidth , Zhai, C. and Lafferty, J. . The two oftenly used smoothing methods; the Gaussian Kernel and Spline are compared. The two smoothing techniques are illustrated and compared using data obtained from Nairobi Securities exchange (NSE) and found that the Gaussian Kernel outperforms the Spline smoother since it gives the best estimate of the variance.

##### On Modified Inverse Shanker Distribution and Applications

Grace O. Nwadiogbu, F. C. Eze, Chrisogonus K. Onyekwere

Asian Journal of Probability and Statistics, Page 46-58
DOI: 10.9734/ajpas/2022/v18i430456

Due to variations in life occurrences, descriptions or interpretations and predictions with some level of accuracy has become challenging. In order to use models to solve these problems, statisticians have provided numerous number of probability distributions which can be used to describe one situation or the other. Rama shanker provided Shanker distribution which is not flexible enough to accommodate datasets with decreasing function. In order to add flexibility to Shankers’ distribution, the aim of this article is to suggest a new model developed by modifying shankers’ distribution. The new distribution will be called “Modified inverse Shanker distribution”. It has one special case, inverse Shanker distribution. Besides the basic properties of the distribution, the maximum likelihood technique of estimating the parameters of the distribution and some of the reliability measures are also discussed. We also illustrate the applicability of the proposed distribution using two real datasets.

##### A Copula-Based Approach for Modelling the Dependence between Inflation and Exchange Rate in Kenya

Kaneza Tracy, Helen Waititu, Stanley Sewe

Asian Journal of Probability and Statistics, Page 59-84
DOI: 10.9734/ajpas/2022/v18i430457

In this study, we modeled the dependence structure between inflation and exchange rate using the copula approach. To formulate a bivariate copula, we used ARMA+GARCH to model serial dependence for each univariate series of returns. Both for in ation and exchange rate, it was found that the student t distribution was the best marginal distribution. Then, we transformed the standardized residuals from those marginal distributions (student t) into uniform over the range [0; 1]. To estimate the copula, we used a parametric approach. Gumbel copula was found to be the best to capture the dependence. We investigated the time-varying dependence using change-point detection based on copula. We found that there is a significant change in the nature of dependence over the period under consideration. The change in the nature of dependence between the two variables was in line with the prevailing macro-economics conditions during the period under review. We recommend to the future researchers to consider studying time-varying dependence between those two variables and investigate also the change in copula parameters in values with time. We also recommend including other macroeconomic variables while modeling the relationship between in ation and exchange rate.