Some estimators of the PMF and CDF of the Logarithmic Series Distribution

TL;DR

This paper compares various statistical estimators for the PMF and CDF of the Logarithmic Series distribution using Monte Carlo simulations to evaluate their performance.

Contribution

It introduces and compares multiple estimators for the Logarithmic Series distribution's PMF and CDF, including UMVUE, MLE, PCE, LSE, and WLSE.

Findings

MLE performs best in certain scenarios

UMVUE provides unbiased estimates

Simulation results guide estimator selection

Abstract

This article addresses the different methods of estimation of the probability mass function (PMF) and the cumulative distribution function (CDF) for the Logarithmic Series distribution. Following estimation methods are considered: uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE), percentile estimator (PCE), least square estimator (LSE), weighted least square estimator (WLSE). Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation.