Normal-Power Function Distribution with Logistic Quantile Function: Properties and Application

Matthew Iwada Ekum¹, Obalowu Job², Jimoh Taylor¹, Asimi Amalare¹, Mundher Abdullah Khaleel³ and Adeyinka Solomon Ogunsanya^2,

¹Department of Mathematics & Statistics, Lagos State Polytechnic Lagos, Nigeria

²Department of Statistics, University of Ilorin, Ilorin, Kwara State, Nigeria

³College of Computer Sciences and Mathematics, Tikrit University, Tikrit, Iraq

Cite this paper:
Matthew Iwada Ekum, Obalowu Job, Jimoh Taylor, Asimi Amalare, Mundher Abdullah Khaleel and Adeyinka Solomon Ogunsanya. Normal-Power Function Distribution with Logistic Quantile Function: Properties and Application. American Journal of Applied Mathematics and Statistics. 2021; 9(3):90-101. doi: 10.12691/ajams-9-3-3

Abstract

Developing compound probability distributions is very important in the field of probability and statistics because there are different datasets from different fields with different features. These features range from high skewness, peakedness (kurtosis), bimodality, highly dispersed, and so on. Existing distributions might not easily fit well to these emerging data of interest. So, there is a need to develop more robust and flexible distributions that are positively skewed, negatively skewed, and bathup shape, to handle some of these features in the emerging data of interest. This paper, therefore, proposed a new four-parameter distribution called the Normal-Power{logistic} distribution. The proposed distribution was characterized by its density, distribution, survival, hazard, cumulative hazard, reversed hazard, and quantile functions. Properties such as the r-th moment, heavy tail property, stochastic ordering, mean inactive time were obtained. A useful transformation of the proposed distribution to normal distribution was shown to help generate its quantiles. The method of Maximum Likelihood Estimation (MLE) was used to estimate the model parameters. A simulation study was carried out to test the consistency of the maximum likelihood parameter estimates. The result of the simulation shows that the biases reduce as the sample size increases for different parameter values. The importance of the new distribution was proved empirically using a real-life dataset of gauge lengths of 10mm. The proposed distribution was compared with five other competing distributions, and the results show that the proposed Normal-Power{logistic} distribution (NPLD) performed favourably than the other five distributions using the AIC, CAIC, BIC, HQIC criteria.

Keywords:
power function distribution normal distribution logistic distribution Normal-Power{logistic} distribution T-R{Y} framework

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