Estimation of the PDF and the CDF of exponentiated moment exponential distribution

Yogesh Mani Tripathi (), Tanmay Kayal and Sanku Dey
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Yogesh Mani Tripathi: Indian Institute of Technology Patna
Tanmay Kayal: Indian Institute of Technology Patna
Sanku Dey: St. Anthony’s College

International Journal of System Assurance Engineering and Management, 2017, vol. 8, issue 2, No 58, 1282-1296

Abstract: Abstract This article addresses the different methods of estimation of the probability density function and the cumulative distribution function for the exponentiated moment exponential distribution. Following estimation methods are considered: uniformly minimum variance unbiased estimators, maximum likelihood estimators, percentile estimators, least squares estimators, weighted least square estimators, maximum product of spacings estimators, Cramér–von-Mises estimators and Anderson–Darling estimators. Analytical expressions are derived for the bias and the mean squared error. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Simulation studies and real data applications show that the ML estimator performs better than others. Finally, one real data set has been analyzed for illustrative purposes.

Keywords: Exponentiated moment exponential distribution; Least squares estimator; Maximum likelihood estimator; Model selection criteria; Percentile estimator; Weighted least squares estimator (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13198-017-0599-3

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