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We examine stochastic inequality probabilities of the form P (X > Y) and P (X > max (Y, Z)) where X, Y, and Z are random variables with beta, gamma, or inverse gamma distributions. We discuss the applications of such inequality probabilities to adaptively randomized clinical trials as well as methods for calculating their values.
The recent paper by Shao et al (2004) claims to have introduced a new model for frequency analysis referred to as the extended Burr XII distribution. The cumulative distribution function (cdf) and the probability density function (pdf) of this new distribution are specified as: { } { }      λ − − λ − − = c k c x x k x F) / (exp 1) / (1 1) (/ 1 0 if 0(More)