Some estimators of the PDF and CDF of the Lindley Distribution

This article addresses the different methods of estimation of the probability density function (PDF) and the cumulative distribution function (CDF) for the Lindley 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), Cram\'{e}r-von-Mises estimator (CVME), Anderson-Darling estimator (ADE). Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation

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

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.Comment: arXiv admin note: substantial text overlap with arXiv:1604.0630

Study on estimators of the PDF and CDF of the one parameter polynomial exponential distribution

In this article, we have considered one parameter polynomial exponential (OPPE) distribution. The exponential, Lindley, length-biased Lindley and Sujatha distribution are particular cases. Two estimators viz, MLE and UMVUE of the PDF and the CDF of the OPPE distribution have been discussed. The estimation issue of the length-biased Lindley and Sujatha distribution have been considered in detail. The estimators have been compared in MSE sense. Monte Carlo simulations and real data analysis are performed to compare the performances of the proposed methods of estimation