We analyze the structure of a random boolean matrix. The corresponding probability distribution is studied with the help of multivariate probability generating functions. This problem is an illustrative example of a class of multivariate functions characterized by a set of diierence-diierential equations which plays an important role in probability theory. We show how to handle and approximate ...

It is known that probability density functions and probability mass functions can usually be calculated quite easily by numerically inverting their transforms (Laplace transforms and generating functions, respectively) with the Fourier-series method, but other more general functions can be substantially more difficult to invert, because the aliasing and roundoff errors tend to be more difficult...

Abstract: In this paper a non-repairable multi-state system with imprecise probabilities and performance rates are taken, representing imprecise probabilities by interval valued probabilities. These intervals are evaluated by computing bound of interval valued ordinary differential equation of the system. For imprecise performance rates random fuzzy variables are introduced. The proposed method...

The Appell-type polynomial family corresponding to the simplest non-commutative derivative operator turns out to be connected with the Boolean probability theory, the simplest of the three universal non-commutative probability theories (the other two being free and tensor/classical probability). The basic properties of the Boolean Appell polynomials are described. In particular, their generatin...

bentea and tu{a}rnu{a}uceanu~(an. c{s}tiinc{t}. univ. al. i.cuza iac{s}, ser. nouv{a}, mat., {bf 54(1)} (2008), 209-220)proposed the following problem: find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$q_8times mathbb{z}_n$ where $q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. in this paper weconsider more general grou...

We consider the set F (n,N) of random forests consisting of n vertices and N rooted trees which can be viewed as realizations of Galton-Watson branching processes with N initial particles and conditioned to have total progeny n. Such forests consist of simply generated trees according to Meir and Moon [20] and therefore they can easily be described by generating functions: Let b(z) = ∑ n≥0 bn,N...

Using an averaged generating function for coloured hard-dimers, some random variables of interest are studied. The main result lies in the fact that all their probability distributions obey a central limit theorem.

The aim of this work is to introduce a modification of chemical graphs fingerprints for data mining. The algorithm reduces the number of features by taking the probability of producing an unique feature at a specific search depth into account. We observed the probability of generating a non-unique feature depending on a search parameter (which leads to a power-law growths of features) and model...

Abstract: This paper is concerned with the analysis of exact symbol error probability (SEP) for cooperative diversity using amplify-and-forward (AF) relaying over independent and non-identical Nakagami-m fading channels. The mathematical formulations for Probability Density Function (pdf) and Moment Generating Function (MGF) of a cooperative link have been derived for calculating symbol error p...

© 2010 ETRI Journal, Volume 32, Number 3, June 2010 In this letter, we analyze the error performance of a mobile communication system with microdiversity and macrodiversity reception in gamma-shadowed Rician fading channels for a binary differential phase-shift keying modulation scheme. Analytical expressions for the probability density function (PDF) and moment-generating function (MGF) are de...