Closed-form approximations for the density and cumulative distribution function of the doubly noncentral t distribution are developed based on saddlepoint methods. They exhibit remarkable accuracy throughout the entire support of the distribution and are vastly superior to existing approximations. An application in finance is considered which capitalizes on the enormous increase in computationa...

Recent advances in quantum key distribution (QKD) have given rise to systems that operate at transmission periods significantly shorter than the dead times of their component single-photon detectors. As systems continue to increase in transmission rate, security concerns associated with detector dead times can limit the production rate of sifted bits. We present a model of highspeed QKD in this...

It is often claimed that the security of quantum key distribution (QKD) is guaranteed by the laws of physics. However, this claim is content-free if the underlying theoretical definition of QKD is not actually compatible with the laws of physics. This paper observes that (1) the laws of physics pose serious obstacles to the security of QKD and (2) the same laws are ignored in all QKD “security ...

Based on the probability generating function of stuttering Poisson distribution (SPD), this paper considers some equivalent propositions of SPD. From this, we show that some distributions in the application of non-life insurance actuarial science are SPD, such as negative binomial distribution, compound Poisson distribution etc.. By weakening condition of equivalent propositions of SPD, we defi...

In our continuous variable quantum key distribution (QKD) scheme, the homodyne detection set-up requires balancing the intensity of an incident beam between two photodiodes. Realistic lens systems are insufficient to provide a spatially stable focus in the presence of large spatial beam-jitter caused by atmospheric transmission. We therefore present an improved geometry for optical tapers which...

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...