# On discrimination between the Lindley and xgamma distributions

## TL;DR

This paper compares the Lindley and xgamma distributions for skewed non-negative data, proposing a likelihood ratio method and deriving asymptotic distributions to determine the sample size needed for accurate discrimination.

## Contribution

It introduces a likelihood ratio approach with asymptotic analysis to effectively distinguish between Lindley and xgamma distributions in data analysis.

## Key findings

- Derived asymptotic distributions of likelihood ratios
- Provided sample size formulas for distribution discrimination
- Enhanced methods for modeling skewed time-to-event data

## Abstract

For a given data set the problem of selecting either Lindley or xgamma distribution with unknown parameter is investigated in this article. Both these distributions can be used quite effectively for analyzing skewed non-negative data and in modeling time-to-event data sets. We have used the ratio of the maximized likelihoods in choosing between the Lindley and xgamma distributions. Asymptotic distributions of the ratio of the maximized likelihoods are obtained and those are utilized to determine the minimum sample size required to discriminate between these two distributions for user specified probability of correct selection and tolerance limit.