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Efficient Estimation of the PDF and the CDF of a Generalized Logistic Distribution

Efficient Estimation of the PDF and the CDF of a Generalized Logistic Distribution The generalized logistic distribution is a useful extension of the logistic distribution, allowing for increasing and bathtub shaped hazard rates and has been used to model the data with a unimodal density. Here, we consider estimation of the probability density function and the cumulative distribution function of the generalized logistic distribution. The following estimators are considered: maximum likelihood estimator, uniformly minimum variance unbiased estimator (UMVUE), least square estimator, weighted least square estimator, percentile estimator, maximum product spacing estimator, Cramér–von-Mises estimator and Anderson–Darling estimator. Analytical expressions are derived for the bias and the mean squared error. Simulation studies are also carried out to show that the maximum-likelihood estimator is better than the UMVUE and that the UMVUE is better than others. Finally, a real data set has been analyzed for illustrative purposes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Data Science Springer Journals

Efficient Estimation of the PDF and the CDF of a Generalized Logistic Distribution

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Business and Management; Business and Management, general; Statistics for Business/Economics/Mathematical Finance/Insurance; Computing Methodologies
ISSN
2198-5804
eISSN
2198-5812
DOI
10.1007/s40745-016-0093-9
Publisher site
See Article on Publisher Site

Abstract

The generalized logistic distribution is a useful extension of the logistic distribution, allowing for increasing and bathtub shaped hazard rates and has been used to model the data with a unimodal density. Here, we consider estimation of the probability density function and the cumulative distribution function of the generalized logistic distribution. The following estimators are considered: maximum likelihood estimator, uniformly minimum variance unbiased estimator (UMVUE), least square estimator, weighted least square estimator, percentile estimator, maximum product spacing estimator, Cramér–von-Mises estimator and Anderson–Darling estimator. Analytical expressions are derived for the bias and the mean squared error. Simulation studies are also carried out to show that the maximum-likelihood estimator is better than the UMVUE and that the UMVUE is better than others. Finally, a real data set has been analyzed for illustrative purposes.

Journal

Annals of Data Science – Springer Journals

Published: Jan 13, 2017

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