# Efficient estimation in the Topp-Leone distribution

## TL;DR

This paper compares various estimators for the Topp-Leone distribution's density and distribution functions, finding the maximum likelihood estimator to be the most efficient based on simulation results.

## Contribution

It introduces and evaluates multiple estimators for the Topp-Leone distribution, highlighting the efficiency of the maximum likelihood estimator.

## Key findings

- MLE outperforms other estimators in efficiency
- Simulation confirms MLE's superior performance
- Provides practical estimators for Topp-Leone distribution

## Abstract

In the current paper, the estimation of the probability density function and the cumulative distribution function of the Topp-Leone distribution is considered. We derive the following estimators: maximum likelihood estimator, uniformly minimum variance unbiased estimator, percentile estimator, least squares estimator and weighted least squares estimator. A simulation study shows that the maximum likelihood estimator is more efficient than the others estimators.