The Stress-Strength Model And Its Generalizations: Theory and Applications

Some Notations and Abbreviations

pdf

probability density function

cdf

cumulative distribution function

edf

empirical distribution function

MLE

maximum likelihood estimation (estimator)

LRT

likelihood ratio test

MSE

mean squared error

EB

empirical Bayes

UMVUE

uniformly minimum variance unbiased estimator

HPD region

highest probability density (region)

BVED

bivariate exponential distribution

WMW statistic

Wilcoxon-Mann-Whitney statistic

ROC curve

receiver operating characteristic curve

OD graph

ordinal dominance graph

the MLE of R

the UMVUE of R

?

the Bayes estimator of R

X

( X 1, , )

Y

( Y 1, , )

~

distributed as

approximately distributed as

?( )

the cdf of the standard normal distribution

?( )

the Gamma function

B( , )

the Beta function

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