Related papers: On a power series distribution with mean parameter…
In order to improve the already existing models that are used extensively in bio sciences and applied sciences research, a new class of Weighted Power function distribution (WPFD) has been proposed with its various properties and different…
We show that the Conway--Maxwell--Poisson distribution can be arbitrarily underdispersed when parametrized via its mean. More precisely, if the mean $\mu$ is an integer then the limiting distribution is a unit probability mass at $\mu$. If…
We have developed a heuristic showing that in the Dirichlet divisor problem for the almost all $n \in \mathbb{N}^{+}$: $$ R(n) \leq O(\psi(n)n^{\frac{1}{4}}) $$ where $$ R(n) = \Big\lvert \sum_{x=1}^{n}\Big\lfloor\frac{n}{x}\Big\rfloor -…
We shall investigate and arrive at a certain functional property of the double series \[ \sum\limits_{n,r\geq 1}\frac{1}{\sqrt{x^2n^2+r^2+w^2}\left( e^{2 \pi y\sqrt{x^2n^2+r^2+w^2}}-1\right)}. \]
In this paper, we derive closed-form exact expressions for the main statistics of the ratio of squared alpha-mu random variables, which are of interest in many scenarios for future wireless networks where generalized distributions are more…
Compound Poisson distributions have been employed by many authors to fit experimental data, typically via the method of moments or maximum likelihood estimation. We propose a new technique and apply it to several sets of published data. It…
Consider random matrices $A$, of dimension $m\times (m+n)$, drawn from an ensemble with probability density $f(\rmtr AA^\dagger)$, with $f(x)$ a given appropriate function. Break $A = (B,X)$ into an $m\times m$ block $B$ and the…
Pyrosequencing is one of the important next-generation sequencing technologies. We derive the distribution of the number of positive signals in pyrograms of this sequencing technology as a function of flow cycle numbers and nucleotide…
This paper proposes a generalized binomial distribution with four parameters, which is derived from the finite capacity queueing system with state-dependent service and arrival rates. This distribution is also generated from the conditional…
In this paper, we introduce the Gompertz power series class of distributions which is obtained by compounding Gompertz and power series distributions. This distribution contains several lifetime models such as Gompertz-geometric,…
We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively…
We calculate the 1-loop renormalization of a set of extended fermionic bilinears which form a basis corresponding to moments of the parton distribution functions. We use the overlap action for fermions and Luescher-Weisz (LW) action for…
The aim of the article is to recover a certain type of finite parametric distributions and functions using their spherical mean transform which is given on a certain family of spheres whose centers belong to a finite set $\Gamma$. For this,…
This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a…
We express generalized Cauchy-Stieltjes transforms of some particular Beta distributions (of ultraspherical type generating functions for orthogonal polynomials) as a powered Cauchy-Stieltjes transform of some measure. For suitable values…
In this paper we introduce a new probability distribution on (0,1), associated with the I-function, namely, the I-function distribution. This distribution generalizes several known distributions with positive support. It is also shown that…
Denote by {$\times$} the fractional part. We establish several new metrical results on the distribution properties of the sequence ({x n }) n$\ge$1. Many of them are presented in a more general framework, in which the sequence of functions…
The power spectrum is traditionally parameterized by a truncated Taylor series: $ln P(k) = ln P_* + (n_*-1) ln(k/k_*) + {1/2} n'_* ln^2(k/k_*)$. It is reasonable to truncate the Taylor series if $|n'_* ln(k/k_*)| << |n_*-1|$, but it is not…
In this paper we consider suitable families of power series distributed random variables, and we study their asymptotic behavior in the fashion of large (and moderate) deviations. We also present two examples of fractional counting…
For a natural number n, let M(n) denote the maximum exponent of any prime power dividing n, and let m(n) denote the minimum exponent of any prime power dividing n. We study the second moments of these arithmetic functions and establish…