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Journal of Probability and Statistics
Volume 2015, Article ID 393608, 11 pages
http://dx.doi.org/10.1155/2015/393608
Research Article

The Type I Generalized Half-Logistic Distribution Based on Upper Record Values

1Department of Statistics, Amity Institute of Applied Sciences, Amity University, Noida 201 303, India
2Department of Statistics, PGDAV College, University of Delhi, Delhi 110007, India

Received 1 June 2015; Revised 9 July 2015; Accepted 26 July 2015

Academic Editor: Shein-chung Chow

Copyright © 2015 Devendra Kumar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the type I generalized half-logistic distribution and derive some new explicit expressions and recurrence relations for marginal and joint moment generating functions of upper record values. Here we show the computations for the first four moments and their variances. Next we show that results for record values of this distribution can be derived from our results as special cases. We obtain the characterization result of this distribution on using the recurrence relation for single moment and conditional expectation of upper record values. We obtain the maximum likelihood estimators of upper record values and their confidence intervals. Also, we compute the maximum likelihood estimates of the parameters of upper record values and their confidence intervals. At last, we present one real case data study to emphasize the results of this paper.