Normal-Power-Logistic Distribution: Properties and Application in Generalized Linear Model

Abstract

The applications of Normal distribution in literature are verse, the new modified univariate normal power distribution is a new distribution which is adequate for modelling bimodal data. There are many data that would have been modelled by normal distribution, but because of their bimodality, they are not, since normal distribution is unimodal. In this paper, a new extension of the normal linear model called the normal-Power generalized linear model, derived from the T-Power Logistic framework is presented. The statistical properties of the distribution and the proposed model were derived such as quantiles, median, mode, robust skewness, robust kurtosis and moment. The maximum likelihood estimation method was considered to obtain the unknown model parameters. Three real data sets were analyzed to demonstrate the flexibility and usefulness of the proposed model. The new model would be very useful as alternative in cases where skewed or bimodal response variables, which are not well fitted with normal linear model.

Some modified estimators for efficient estimation of power function model

“…Dorp and Kotz 4 (2002) applied the distribution in financial engineering. The applicability of the Power Function model in different fields has also been documented in many other studies 5–8 …”

“…The applicability of the Power Function model in different fields has also been documented in many other studies. [5][6][7][8] The Power Function distribution can be expressed with two parameters that is, scale parameter (𝛽) and shape parameter(𝛾). Let 𝑥 1 , 𝑥 2 , 𝑥 3 … … … ..𝑥 𝑛 be a random sample from the two-parameter Power Function distribution having probability density function (pdf) and Cumulative Distribution Function (CDF) as 𝑓 (𝑥; 𝛾, 𝛽) = 𝛾𝑥 𝛾−1 𝛽 𝛾 , where 0 ≤ 𝑥 ≤ 𝛽 and 𝛾, 𝛽 > 0.…”