We give exact closed-form expressions for the Kolmogorov and total variation distances between Poisson, binomial, negative binomial distributions with different parameters. In Poisson case, such are related Lambert function.

The Muth distribution is a continuous random variable introduced in the context of reliability theory. In this paper, some mathematical properties model are derived, including analytical expressions for moment generating function, moments, mode, quantile function and moments order statistics. regard, generalized integro-exponential Lambert W golden ratio arise natural way. parameter estimation performed by methods maximum likelihood, least squares, weighted squares which compared via Monte...

Muth introduced a probability distribution with application in reliability theory. We propose new model from the law. This paper studies its statistical properties, such as computation of moments, computer generation pseudo-random data and behavior failure rate function, among others. The estimation parameters is carried out by method maximum likelihood Monte Carlo simulation study assesses performance this method. practical usefulness illustrated means two real sets, showing that it may...

Abstract Given a finite set of N nodes and the time required for traveling among nodes, in repairman problem, we seek route that minimizes sums delays reaching each node. In this note, present linear algorithm solving problem when underlying graph is path, improving Θ( 2 ) space complexity previously best problem. We also provide walk with deadlines (WPD) on paths. © 2002 Wiley Periodicals, Inc.

The shifted Gompertz distribution was introduced by Bemmaor (1994 , A. C. ( 1994 ). Modelling the diffusion of new durable goods: Word-of-mouth effect versus consumer heterogeneity . In: Laurent G. Lilien L. Pras B. eds. Research Traditions in Marketing Boston : Kluwer pp. 201 – 229 [Google Scholar]) as a random model adoption timing innovations market. purpose this article is threefold. We provide explicit expressions for expectation and variance model, which are functions Euler constant....

Abstract A two-parameter probability distribution with bounded support is derived from the shifted Gompertz distribution. It shown that this model corresponds to of minimum a random number Poisson independent variables having common power function Some statistical properties are written in closed form, such as moments and quantile function. To end, incomplete gamma Lambert W play central role. The shape failure rate mean residual life studied. Analytical expressions also provided for order...

In this paper, we consider the sequence $(\theta _n)_{n\ge 0}$ solving Ramanujan equation \[ \frac {e^n}{2}=\sum _{k=0}^{n}\frac {n^k}{k!}+\frac {n^n}{n!} (\theta _n-1),\qquad n=0,1,\dots . \] The three main achievements are following. We introduce a continuous–time extension $\theta (t)$ of _n$ and show its close connections with medians $\lambda $\Gamma (n+1,1)$ distributions Charlier polynomials. give upper lower bounds for both _n$, in particular which sharper than other known...

We provide an explicit analytical solution for a logarithmic integral in terms of the Lerch transcendent function together with generalized Stirling numbers first kind. For some special cases interest statistical applications, can be expressed polylogarithm aforementioned numbers. As consequence, we obtain expressions moments order statistics from half-logistic distribution, Weibull-geometric distribution and long-term which include as particular extended exponential-geometric among others....

The aim of this paper is twofold. First, we show that the expected value minimum order statistic from Gompertz-Makeham distribution can be expressed in closed form terms incomplete gamma function. We also give a general formula for moments generalized integro-exponential As consequence, all statistics probability more easily evaluated statistic. Second, maximum and are domains attraction Gumbel Weibull distributions, respectively. Lambert W function plays an important role solving these problems.

The purpose of this paper is to establish a connection between the polylogarithm function and continuous probability distribution. We provide closed-form expressions in terms for all moments random variable related Bass diffusion model, which was introduced by widely used marketing science. In addition, new integral representation order n achieved from probabilistic formulation.

Many models of asymmetric distributions proposed in the statistical literature are obtained by transforming an arbitrary symmetric distribution means a skewing mechanism. In certain important cases, resultant skewed shares some properties its antecedent. Because this inheritance, it would be interesting to test if generator belongs family, that is say, testing goodness‐of‐fit for component. This work proposes such hypothesis. Taking into account normal law perhaps most studied distribution,...