American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: Editor-in-chief: Mohamed Seddeek
Open Access
Journal Browser
American Journal of Applied Mathematics and Statistics. 2014, 2(3), 121-128
DOI: 10.12691/ajams-2-3-6
Open AccessArticle

Inference on P(X < Y) for Extreme Values

Sudhansu S. Maiti1, and Sudhir Murmu2

1Department of Statistics, Visva-Bharati University Santiniketan, India

2District Rural Development Agency Khunti, Jharkhand, India

Pub. Date: May 03, 2014

Cite this paper:
Sudhansu S. Maiti and Sudhir Murmu. Inference on P(X < Y) for Extreme Values. American Journal of Applied Mathematics and Statistics. 2014; 2(3):121-128. doi: 10.12691/ajams-2-3-6


The article considers the problem of , when X and Y belong to independently distributed two extreme value distributions. Maximum likelihood estimate of R has been found out and the estimates assuming different distributions have been compared for complete samples. Lower confidence limits of R have been found out by Delta method and bootstrap method. The Bayes estimate of R has also been calculated using MCMC approach.

Bayes estimate delta method Lower Confidence Limit Metropolis-Hastings algorithm

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


[1]  Congdon, P., Bayesian Statistical Modeling, John Wiley, , 2001.
[2]  Efrom, B., The jackknife, the bootstrap and other resampling plans, In CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Phiadelphia, PA, 3, 1982.
[3]  Efron, B., Discussion: Theoritical comparison of bootstrap intervals, The Annals of Statistics, 16, 969-972, 1988.
[4]  Hall, P. Theoritical comparison of bootstrap confidence intervals, Annals of Statistics, 16, 927-953, 1988.
[5]  McCool, I.J., Inference o P(X<Y) in the Weibull case, Commun. Statist.-Simula. and Comp., 20, 129-148, 1991.
[6]  Mukherjee, S.P. and Maiti, S.S., Stress-Strength reliability in the Weibull case, Frontiers in reliability, World Scientific, 4, 231-248, 1998.