# Topp-Leone generated q-exponential distribution and its applications

## TL;DR

This paper introduces a new family of lifetime distributions called the Topp-Leone generated q-exponential family, providing methods for parameter estimation and demonstrating its flexibility and effectiveness with real data.

## Contribution

It presents a novel distribution family based on Topp-Leone and q-exponential, with estimation techniques and empirical validation.

## Key findings

- The new distribution model is flexible and effective for lifetime data.
- Maximum likelihood and Bayesian methods are used for parameter estimation.
- Empirical analysis shows the model's applicability to real data.

## Abstract

Topp-Leone distribution is a continuous model distribution used for modelling lifetime phenomena. The main purpose of this paper is to introduce a new framework for generating lifetime distributions, called the Topp-Leone generated q-exponential family of distributions. Parameter estimation using maximum likelihood method and simulation results to assess effectiveness of the distribution are discussed. Different informative and non-informative priors are used to estimate the shape parameter of q extended Topp-Leone generated exponential distribution under normal approximation technique. We prove empirically the importance and flexibility of the new model in model building by using a real data set.