The negative binomial distribution has become increasingly popular as a more flexible alternative to Poisson distribution, especially when it is questionable whether the strict requirements for Poisson distribution could be satisfied. But negative binomial distribution is better for overdispersed count data that are not necessarily heavy-tailed, for heavy tailed count data the traditional stati...

A.S. Trushechkin, 2, 3 P.A. Tregubov, E.O. Kiktenko, 4 Y.V. Kurochkin, 3 and A.K. Fedorov 3, 5 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 Russian Quantum Cent...

We examined time-dependent statistical properties of electromyographic (EMG) signals recorded from intrinsic hand muscles during handwriting. Our analysis showed that trial-to-trial neuronal variability of EMG signals is well described by the lognormal distribution clearly distinguished from the Gaussian (normal) distribution. This finding indicates that EMG formation cannot be described by a c...

With the help of a simple quantum key distribution (QKD) scheme, we discuss the relation between BB84-type protocols and two-step-type ones. It is shown that they have the same essence, i.e., information-splitting. More specifically, the similarity between them includes (1) the carrier state is split into two parts which will be sent one by one; (2) the possible states of each quantum part are ...

It is demonstrated that in a two-stage scenario with elementary Poissonian emitters of particles (colour strings) arbitrarily distributed in their number and average multiplicities, the forward-backward correlations are completely determined by the final distribution of forward particles. The observed linear form of the correlations then necessarily requires this distribution to have a negative...

To enable global scale quantum key distribution (QKD), satellite based systems are the most promising approach. So far, free-space QKD has already been demonstrated on communication channels with attenuation comparable to satellite downlinks, and classical laser communications with satellites and aircrafts is heavily explored. Here, combining both these challenges, we demonstrate an aircraft to...

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In this article we construct bivariate discrete distribution in Z. We make use of a generalized trivariate reduction technique. The special case leading to bivariate Skellam distributions is studied in detail. Properties of the derived models as well as estimation are examined. Real data application is provided. Discussion of extensions to different models is also mentioned.