We derive a quantile-adjusted conditional maximum likelihood estimator for the dispersion parameter of the negative binomial distribution and compare its performance, in terms of bias, to various other methods. Our estimation scheme outperforms all other methods in very small samples, typical of those from serial analysis of gene expression studies, the motivating data for this study. The impac...

In this paper, we present three generalized quantum key distribution protocols between two groups, which consist of k and l members respectively. In these protocols two groups retrieve the secure key string, only if all members should cooperate with one another in each group. We show that if there is an eavesdropper between two groups then their cheating or eavesdropping cannot be accomplished.

In a typical optical implementation of the Bennett-Brassard 1984 (so-called BB84) quantum key distribution protocol, the sender uses an active source to produce the required signal states. While active state preparation of BB84 signals is a simple and elegant solution in principle, in practice passive state preparation might be desirable in some scenarios, for instance, in those experimental se...

We assume that product i has a constant hazard of adjusting, fi, in each month, where fi ∼ Beta(a, b). Let us denote the product’s lifetime by ni. These assumptions imply that the total number of price changes in a product’s lifetime is distributed according to the binomial distribution, xi ∼ Bin(ni, fi). We assume, furthermore, that fi is distributed according to the beta distribution, fi ∼ Be...

A.S. Trushechkin, 2, 3 E.O. Kiktenko, 4 and A.K. Fedorov 5, 6 Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia National Research Nuclear University MEPhI, Moscow 115409, Russia Department of Mathematics and Russian Quantum Center, National University of Science and Technology MISiS, Moscow 119049, Russia Bauman Moscow State Technical University, Moscow 105005...

Consider k success counts from a binomial distribution with unknown N and success probability p. We consider the problem of estimating N. By integrating the likelihood for Nand p over a beta density for p, we obtain the beta-binomial distribution which results in stable and reasonably efficient estimators of N, which compare favorably with and are often better than the estimates introduced by O...

In this paper, we are concerned with the situations, where sometimes value two is reported erroneously as one in relation to size biased generalized negative binomial distribution (SBGNBD) with probability αα. We have obtained the Maximum likelihood estimator and Bayes estimator under general entropy loss function. A simulated study is carried out to access the performance of the maximum likeli...

The number of new gadolinium-enhancing lesions discovered via magnetic resonance imaging is a well-established outcome for multiple sclerosis studies, especially Phase II Studies. Due to the high cost of magnetic resonance imaging scans, many investigators select participants for the presence of lesions. While this selection procedure is thought to improve the power of inferences, the effect of...