This paper provides exact probability results for waiting times associated with occurrences of two types of motifs in a random sequence. First, we provide an explicit expression for the probability generating function of the interarrival time between two clumps of a pattern. It allows, in particular, to measure the quality of the Poisson approximation which is currently used for evaluation of t...

A generalized probability distribution is developed which served as a general formula for some well known probability distributions such as weibull, exponential, rayleigh. gamma, log-nonnal. pareto. maxwell, generalized laplace etc. Besides aforesaid probahility distributions, a family of new disuibutions can also be derived from it. The statistical properties viz. moments and moment generating...

We study a two-type branching process which provides an excellent description of experimental data on cell dynamics in skin tissue. The model involves only a single type of progenitor cell, that is it does not require support from a self-renewed population of stem cells. The progenitor cells divide and may differentiate into post-mitotic cells. We derive an exact solution for the generating fun...

In this paper ,we discuss the Geom/G/1 queue with Bernoulli feedback and server setup/closedown times.We derive the probability generating function (PGF) of the steady-state queue length immediately after a service completion by the embedded Markov chain and the PGF of the queue length immediately after an arbitrary slot boundary .We also get the PGF of the stationary waiting times under first ...

This paper develops an analytic theory for the study of some Pólya urns with random rules. The idea is to extend the isomorphism theorem in Flajolet et al. (2006), which connects deterministic balanced urns to a differential system for the generating function. The methodology is based upon adaptation of operators and use of a weighted probability generating function. Systems of differential equ...

Exact closed-form expressions are obtained for the outage probability of maximal ratio combining in η − μ fading channels with antenna correlation and co-channel interference. The scenario considered in this work assumes the joint presence of background white Gaussian noise and independent Rayleigh-faded interferers with arbitrary powers. Outage probability results are obtained through an appro...

Generation of Wigner functions of Landau levels and determination of their symmetries and generic properties are achieved in the autonomous framework of deformation quantization. Transformation properties of diagonal Wigner functions under space inversion, time reversal and parity transformations are specified and their invariance under a four-parameter subgroup of symplectic transformations ar...

We consider steady-state current activity statistics for the one-dimensional totally asymmetric simple exclusion process. With the help of the known operator algebra (for general open boundary conditions), as well as general probabilistic concepts (for the periodic case), we derive and evaluate closed-form expressions for the lowest three moments of the probability distribution function. These ...

For the Lego discrepancy with M bins, which is equivalent with a χ2-statistic with M bins, we present a procedure to calculate the moment generating function of the probability distribution perturbatively if M and N , the number of uniformly and randomly distributed data points, become large. Furthermore, we present a phase diagram for various limits of the probability distribution in terms of ...