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

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

Annals of Data Science, 2017, vol. 4, issue 1, No 4, 63-81

Abstract: 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.

Keywords: Generalized logistic distribution; Maximum likelihood estimator; Uniformly minimum variance unbiased estimator; Maximum product spacing estimator; Least square estimator; 62F10 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s40745-016-0093-9

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