A unified treatment is presented here of compounding with the bivariate Poisson distribution. Exploiting the exponential nature of its probability generating function, it is shown that the pgf of the compound distribution is the moment generating function of the compounding random variable. This relationship leads to rather interesting general results. Particularly, the development of the condi...

Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One possible approaches is represented by first-order, non-negative, integer-valued autoregressive processes with zero-and-one innovations, abbr. ZOINAR(1) processes, introduced recently, around year 2020 to present. This manuscript presents a generalization ZOINAR given introd...

In [KL] it is provcd that the probability of two randomly chosen elements of a finite dassical simple group G actually generating G tends to 1 as lei increases. If gEe, let Pu(g) be the probability that, if h is chosen randomly in G, then (g, h) IG. Let PG : = ma..x{Pu(g) I 9 E e#}. In [KL, Conjecture 2] it is suggested that a stronger result might hold: Pc ---4 0 as IGI ---4 00 for simple clas...

A key problem in computational proteomics is distinguishing between correct and false peptide identifications. We argue that evaluating the error rates of peptide identifications is not unlike computing generating functions in combinatorics. We show that the generating functions and their derivatives ( spectral energy and spectral probability) represent new features of tandem mass spectra that,...

We take a general approach to uncertainty on product spaces, and give sufficient conditions for the independence structures of uncertainty measures to satisfy graphoid properties. Since these conditions are arguably more intuitive than some of the graphoid properties, they can be viewed as explanations why probability and certain other formalisms generate graphoids. The conditions include a suf...

Random quanti t ies of interest in operations research models can often be determined conveniently in the form of transforms. Hence, numerical t ransform inversion can be an effective way to obtain desired numerical values of cumulative distribution functions, probability density functions and probability mass functions. However, numerical transform inversion has not been widely used. This lack...

In [2], Dixon considered the following question: " Suppose two permutations are chosen at random from the symmetric group Sn of degree n. What is the probability that they will generate Sn? " Actually, Netto conjectured last century that almost all pairs of elements from Sn will generate Sn or An. Dixon showed that this is true in the following sense: The proportion of ordered pairs (x, y) (x, ...

Let G be a finite group, and let φk(G) be the probability that k random group elements generate G. Denote by θ(G) the smallest k such that φk(G) > 1/e. In this paper we analyze quantity θ(G) for different classes of groups. We prove that θ(G) ≤ κ(G)+ 1 when G is nilpotent and κ(G) is the minimal number of generators of G. When G is solvable we show that θ(G) ≤ 3.25κ(G) + 107. We also show that ...