In the asymptotic theory of quantum hypothesis testing, the error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states, in an increasing way. This is well known as the direct part and strong converse of quantum Stein’s lemma. Here we look into the behavior of this sudden change and h...

BACKGROUND Two- or three-stage designs are commonly used in phase II cancer clinical trials. These designs possess good frequentist properties and allow early termination of the trial when the interim data indicate that the experimental regimen is inefficacious. The rigid study design, however, can be difficult to follow exactly because the response has to be evaluated at prespecified fixed num...

Let X = (Xk)k=0,1,... denote the jump chain of the block counting process of the Λ-coalescent with Λ = β(2 − α, α) being the beta distribution with parameter α ∈ (0, 2). A solution for the hitting probability h(n,m) that the chain X ever visits the state m, conditional that it starts in the state X0 = n, is obtained via an analytic method based on generating functions. For α ∈ (1, 2) the result...

This paper considers parameter estimations in Lomax distribution under progressive type-II censoring with random removals, assuming that the number of units removed at each failure time has a binomial distribution. The maximum likelihood estimators (MLEs) are derived using the expectation-maximization (EM) algorithm. The Bayes estimates of the parameters are obtained using both the squared erro...

The reliability function of arbitrary single-user communication channels is analyzed. A general formula for the partitioning upper bound to the reliability function of channels without feedback is rst established. This bound is indeed a consequence of the recently derived general expression for the Neyman-Pearson type-II error exponent subject to an exponential bound on the type-I error probabi...