Transmuted Lindley-Geometric Distribution and its applications

TL;DR

This paper introduces a new flexible probability distribution called the Transmuted Lindley-Geometric distribution, created via a quadratic rank transmutation map, and demonstrates its applicability to real-world data modeling.

Contribution

The paper develops a novel distribution by applying quadratic rank transmutation to the Lindley geometric distribution, enhancing modeling flexibility.

Findings

The new distribution effectively models real-world data.

Analytical properties of the distribution are derived.

The distribution offers increased flexibility over existing models.

Abstract

A functional composition of the cumulative distribution function of one probability distribution with the inverse cumulative distribution function of another is called the transmutation map. In this article, we will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking Lindley geometric distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. It will be shown that the analytical results are applicable to model real world data.