Open Access Original Research Article

The Effects of Omitted Variable on Multicollinearity in Hierarchical Linear Modelling

V. G. Jemilohun

Asian Journal of Probability and Statistics, Page 1-13
DOI: 10.9734/ajpas/2021/v14i430333

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.

Open Access Original Research Article

Modelling Claim Frequency in Insurance Using Count Models

A. Adetunji Ademola, Shamsul Rijal Muhammad Sabri

Asian Journal of Probability and Statistics, Page 14-20
DOI: 10.9734/ajpas/2021/v14i430334

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.

Open Access Original Research Article

The Type I Half Logistic Skew-t Distribution: A Heavy-Tail Model with Inverted Bathtub Shaped Hazard Rate

O. D. Adubisi, A. Abdulkadir, H. Chiroma, U. F. Abbas

Asian Journal of Probability and Statistics, Page 21-40
DOI: 10.9734/ajpas/2021/v14i430336

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.

Open Access Original Research Article

Rationalization of the Pattern of Rural Out Migration: An Application of a Composite and In ated Probability Models

Brijesh P. Singh, Sandeep Singh, Utpal Dhar Das

Asian Journal of Probability and Statistics, Page 41-51
DOI: 10.9734/ajpas/2021/v14i430337

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.

Open Access Original Research Article

Modified Class of Estimator for Finite Population Mean Under Two-Phase Sampling Using Regression Estimation Approach

A. Y. Erinola, R. V. K. Singh, A. Audu, T. James

Asian Journal of Probability and Statistics, Page 52-64
DOI: 10.9734/ajpas/2021/v14i430338

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.