Open Access Original Research Article

Modelling and Optimization of Portfolio in a DC Scheme with Return of Contributions and Tax using Weibull Force Function

Njoku, K. N. C., Akpanibah, E. E.

Asian Journal of Probability and Statistics, Page 1-12
DOI: 10.9734/ajpas/2022/v16i330401

One of the major challenges faced by most pension fund managers in the defined pension (DC) scheme is how best member’s contributions can be invested to yield maximum returns. To achieve this, there is need to model and developed a robust investment plan which takes into consideration the volatility of the stock market price, tax on investment on risky assets and the mortality risk of its members. Based on this, the optimal portfolio distribution of a DC pension scheme with return of premium clause is studied where the mortality force function is characterized by the Weibull model and the investment in risky asset is subject to a certain proportion of tax. A portfolio with a risk-free asset and a risky asset modeled by the geometric Brownian motion such that the remaining accumulations are equally distributed between the remaining members is considered. Furthermore, the game theoretic approach is used to establish an optimization problem from the extended Hamilton Jacobi Bellman (HJB) equation which is a non-linear partial differential equation (PDE). Using variable separation method, closed form solutions of the optimal portfolio distribution and the efficient frontier are obtained. Lastly, some numerical simulations are used to study the impact of some the parameters on the optimal portfolio distribution with observations that the optimal portfolio distribution developed by the fund manager is inversely proportional to the tax imposed on the risky asset, risk averse coefficient, initial fund size, and risk free interest rate but directly proportional to time.

Open Access Original Research Article

Chen Software Reliability Growth Model

Mumuni Napari Hanifatu, Suleman Nasiru, Jakperik Dioggban

Asian Journal of Probability and Statistics, Page 13-25
DOI: 10.9734/ajpas/2022/v16i330402

Software reliability analysis is very vital in software development. Software manufacturers assess the quality of their developed software through this analysis. This has triggered the development of reliability models. Software reliability growth models have been used extensively to examine the quality of manufactured software before they are sent to the market. This study presents a new software reliability growth model using Chen distribution. The Chen software reliability growth model is then used to establish sequential probability ratio test limits for determining whether a manufactured software is reliable or unreliable. The applications of the proposed model revealed that it performs better than some of the existing software reliability growth models for the given datasets.

Open Access Original Research Article

On A Method of Bias Reduction in the Product Method of Estimation

R. K. Sahoo, Ajit Kumar Sabat, L. N. Sahoo

Asian Journal of Probability and Statistics, Page 26-35
DOI: 10.9734/ajpas/2022/v16i330403

In this paper, we focused our attention on the creation of an almost unbiased predictive product estimator after estimating and correcting bias of the classical product estimator under predictive approach. Considering mean square error as the performance measure, superiority of the proposed estimator has been analyzed compared to the classical product estimator and Robson’s [1] unbiased product estimator under (i) a finite population set-up, (ii) an infinite population set-up assuming bivariate normal distribution between the variables, and (iii) the assumption of a super-population model.

Open Access Original Research Article

Response Surface Optimization of Dietary Iron, Calcium and Vitamin C in Soyamilk for Complementary Feeding

Udoudo Unyime Patrick, Chisimkwuo John, Loveline Okoro

Asian Journal of Probability and Statistics, Page 36-53
DOI: 10.9734/ajpas/2022/v16i330404

Response surface methodology (RSM) is a collection of tools developed in the 1950s for the purpose of determining optimum operating conditions. In this work, a three level three factor (33) factorial design that metamorphosed to the response surface design with two augmented central point was employed. In its applications a secondary data from the department of Food Science and Technology (FST), Michael Okpara University of Agriculture, Umudike (MOUAU), containing the mineral components of soymilk for complementary feeding of infants was used. The analysis for the First Order (FO), Two Way Interaction (TWI) and the Polynomial (PQ) model was carried out and the augmented response surface analysis was performed. Following the path of steepest ascent, an optimality condition from the surface and contour lines shows that dietary iron is significant for varying the colour content, while calcium was significant for varying the ash and moisture content. It was then recommended that for optimal colour content in the soymilk, 3.07mg/100ml of Dietary Iron, 154.1mg/100ml of Calcium and 24.23mg/100ml of Vitamin C should be used, for optimal ash content in the soymilk, 2.22mg/100ml of Dietary Iron, 152.03mg/100ml of Calcium and 13.53mg/100ml of Vitamin C should be used while for optimal moisture content in the soymilk, 2.9858mg/100ml of dietary Iron, 335.71mg/100ml of Calcium and 25.48mg/100ml of Vitamin C should be used.

Open Access Original Research Article

New Zero -Truncated Distribution: Properties and Applications

Ahlem Ghouar, Halim Zeghdoudi, Mohammed Cherif Bouras

Asian Journal of Probability and Statistics, Page 54-66
DOI: 10.9734/ajpas/2022/v16i330405

A new zero-truncated distribution called zero-truncated Poisson-Pseudo Lindley distribution is introduced. Its statistical properties including general expression of probabilities, moments, cumulative function and the quantile function were examined. Different statistical properties of moment method, maximum likelihood estimation and the quantile function are identified. The parameters estimation of the zero-truncated Poisson-Pseudo Lindley distribution is explained by estimation methods and, to recommend its performance, a simulation is proposed. The model distribution to real-life data is presented and measured with the goodness of fit got by well-known one and two parameters distributions.