Study on estimators of the PDF and CDF of the one parameter polynomial exponential distribution
Indrani Mukherjee, Sudhansu S. Maiti, Vijay Vir Singh
TL;DR
This paper investigates the estimation of the PDF and CDF of the one parameter polynomial exponential distribution, comparing MLE and UMVUE estimators through simulations and real data analysis.
Contribution
It introduces and compares MLE and UMVUE estimators for the OPPE distribution and its special cases, providing a detailed analysis and performance comparison.
Findings
MLE and UMVUE estimators are compared in terms of MSE.
Monte Carlo simulations demonstrate estimator performance.
Real data analysis validates the estimators' effectiveness.
Abstract
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.
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Taxonomy
TopicsStatistical Distribution Estimation and Applications · Probabilistic and Robust Engineering Design · Bayesian Methods and Mixture Models