On type III generalized half logistic distribution

TL;DR

This paper introduces a new type III generalized half logistic distribution, deriving its key statistical properties to expand the flexibility and applicability of logistic models in statistical analysis.

Contribution

It proposes a novel generalized form of the half logistic distribution, providing its probability functions and moments for the first time.

Findings

Derived the probability density and cumulative distribution functions.

Calculated the moments, median, and mode of the distribution.

Established order statistics for the new distribution.

Abstract

It is well known that generalized models is attracting the attention of researchers in recent times because of their flexibilities. Particularly, the logistic model has been generalized and applied by many authors while the half logistic distribution has not recieve much attention in term of its generalization. In this paper, we considered a generalized form of half logistic model called type III generalized half logistic distribution. We obtained its probability density function, the cumulative distribution function, the $n^{th}$ moment, the median, the mode, the 100$p$-percentage points and the order statistics of the generalized distribution are established.