Open Access Original Research Article

On Generalized Moment Exponential Distribution and Power Series Distribution

Zafar Iqbal, Noreen Ali, Abdur Razaq, Tassaddaq Hussain, Muhammad Salman

Asian Journal of Probability and Statistics, Page 1-21
DOI: 10.9734/ajpas/2020/v6i130150

In this research paper, a new life time family is introduced. Sadaf [1] proposed a moment exponential power series (MEPS) distribution. Generalized moment exponential power series (GMEPS) distribution is a general form of MEPS distribution. It is characterized by compounding GME distribution and power series (PS) distribution. This new family has some new sub models such as GME geometric distribution, GME Poisson (GMEP) distribution, GME logarithmic (GMEL) distribution and GME binomial (GMEB) distribution. We provide statistical properties of GMEPS family of distributions. We find here expression of quantile function based on Lambert W function, the density function of rth order statistic and moments of GMEPS distribution. Descriptive expressions of Shannon entropy and Rényi entropy of new general model are found. We provide special sub-models of the GMEPS family of distributions. The maximum likelihood (ML) estimation method is used to find estimates of the parameters of GMEPS distribution. Simulation study is carried out to check the convergence of new estimators. We apply GMEPS family of distributions on two sets of real data.

Open Access Original Research Article

Multicollinearity Effect in Regression Analysis: A Feed Forward Artificial Neural Network Approach

C. P. Obite, N. P. Olewuezi, G. U. Ugwuanyim, D. C. Bartholomew

Asian Journal of Probability and Statistics, Page 22-33
DOI: 10.9734/ajpas/2020/v6i130151

In this study we compared the performance of Ordinary Least Squares Regression (OLSR) and the Artificial Neural Network (ANN) in the presence of multicollinearity using two datasets – a real life insurance data and a simulated data – to know which of the methods, models a highly correlated dataset better using the Root Mean Square Error (RMSE) as the performance measure. The ANN performed better than the OLSR model for all the different ANN models except the models with nine and ten nodes in the hidden layer for the real life data. The network with four hidden nodes was the best model. For the simulated data, the ANN model with two hidden nodes gave us the least RMSE when compared to the OLSR model and the other ANN models in the testing set. The network with two hidden nodes modelled the data very well. In the presence of multicollinearity, ANN model achieves a better fit and forecast than the OLSR.

Open Access Original Research Article

Mathematical Modeling and Distribution Design for Agricultural Products in Bangladesh

Mohammad Khairul Islam, Md. Mahmud Alam, Mohammed Forhad Uddin, Gazi Mohammad Omar Faruque

Asian Journal of Probability and Statistics, Page 34-42
DOI: 10.9734/ajpas/2020/v6i130152

In this paper, we have formulated a mixed integer linear programming (MILP) model for the distribution design of Agricultural products in Bangladesh. The scheme of distribution is very important for the supply chain network (SCN), which is choosing the suitable distribution center (DC) for the distribution of the products. This study is a real life distribution problem. To developed this model, we have collected data from various market players who are directly or indirectly involved in Agriculture sector. We have to solve this model, by using a mathematical programming language (AMPL). We have verified a multi-stage SCN, which includes producer, DC and customer. Also this model is to optimize profit, allocations of the products and most useable DC which satisfied most of the customer demands. Finally, we can analyze the profit for the uncertainty parameters.

Open Access Original Research Article

On Application of Matlab on Efficient Portfolio Management for a Pension Plan in the Presence of Uneven Distributions of Accumulated Wealth

Obasi, Emmanuela C. M., Akpanibah, Edikan E.

Asian Journal of Probability and Statistics, Page 43-54
DOI: 10.9734/ajpas/2020/v6i130153

In this paper, we solved the problem encountered by a pension plan member whose portfolio is made up of one risk free asset and three risky assets for the optimal investment plan with return clause and uneven distributions of the remaining accumulated wealth. Using mean variance utility function as our objective function, we formulate our problem as a continuous-time mean–variance stochastic optimal control problem. Next, we used the variational inequalities methods to transform our problem into Markovian time inconsistent stochastic control, to determine the optimal investment plan and the efficient frontier of the plan member. Using mat lab software, we obtain numerical simulations of the optimal investment plan with respect to time and compare our results with an existing result.

Open Access Original Research Article

Prediction of the Effect of Demographic Characteristics on Parity Using Poisson Regression Model

C. M. Gatwiri, M. M. Muraya, L. K. Gitonga

Asian Journal of Probability and Statistics, Page 55-63
DOI: 10.9734/ajpas/2020/v6i130154

There is growing interest among the public in demography since demographic change has become the subject of political debates in many countries. Statistics on demography are used to support policy-making and monitor demographic behaviour of political, economic, social and cultural perspectives. Most studies have used descriptive statistics to study demographic characteristics. Moreover, most of these studies investigate effects of individual character at a time. Therefore, there is a need to come up with more robust statistical methods, such as predictive models for demographic studies. The objective of this study was to predict the effect of demographic characteristics on parity using Poisson regression model. Secondary data on parity, age, marital status and education level was collected from Chuka and Embu hospital maternal units from 2013 to 2017. The data was analysed using R-statistical software. Three Poisson regression models (PRMs) were fitted. The likelihood ratio test of all the Poisson regression models had p-values < 0.05 indicating that all the models were statistically significant. Deviance test and Akaike Information Criterion (AIC) were used to assess the fit of Poisson regression models. The overall Poisson model had residual deviance of 184.23, which was the lowest of all other fitted PRM models, suggesting that it was the best fit. The AIC of the PRM with both education and marital status as the predictors had the lowest AIC value of 2078.620, indicating that it was the best fitted model. The dispersion test proved that PRM was not over-dispersed, confirming the model as a good fit of the data. The improved model can be used in prediction of population growth rates.