Related papers: On a power series distribution with mean parameter…
Let $X$ be a random variable with distribution function $F,$ and $X_{1},X_{2},...,X_{n}$ are independent copies of $X.$ Consider the order statistics $X_{i:n},$ $i=1,2,...,n$ and denote $F_{i:n}(x)=P\{X_{i:n}\leq x\}.$ Using majorization…
A new characterization for power function distributions is obtained which is based on products of order statistics. This result may be considered as a generalization of some recent results for contractions. We note that in this new result…
The efficient modeling for disorder in a phenomena depends on the chosen score and objective functions. The main parameters in modeling are location, scale and shape. The exponential power distribution known as generalized Gaussian is…
We propose a two-parameter bounded probability distribution called the extended power distribution. This distribution on $(0, 1)$ is similar to the beta distribution, however there are some advantages which we explore. We define the moments…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Although its probability mass function (pmf) is known, what is lacking is a $visual$…
The probability distribution P(k) of the sizes k of critical trees (branching ratio m=1) is well known to show a power-law behavior k^(-3/2). Such behavior corresponds to the mean-field approximation for many critical and self-organized…
Given an increasing sequence of integers a(n), it is known (due to Weyl) that for almost all reals t, the fractional parts of the dilated sequence t*a(n) are uniformly distributed in the unit interval. Some effort has been made recently to…
During last two decades it has been discovered that the statistical properties of a number of microscopically rather different random systems at the macroscopic level are described by {\it the same} universal probability distribution…
Any power series with nonnegative coefficients has an associated family of probability distributions supported on the nonnegative integers. There is a close connection between the function theoretic properties of the power series and the…
The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformation of a random variable with the standard normal…
There are some real life issues that are exists in nature which has early failure. This type of problems can be modelled either by a complex distribution having more than one parameter or by finite mixture of some distribution. In this…
We investigate fractional moments and expectations of power means of complex-valued random variables by using fractional calculus. We deal with both negative and positive orders of the fractional derivatives. The one-dimensional…
Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…
In this paper, we introduce the Birnbaum-Saunders power series class of distributions which is obtained by compounding Birnbaum-Saunders and power series distributions. The new class of distributions has as a particular case the…
Let $X_1,\ldots,X_M$ and $Y_1,\ldots,Y_N$ be independent zero mean normal random variables with variances $\sigma_{X_i}^2$, $i=1,\ldots,M$, and $\sigma_{Y_j}^2$, $j=1,\ldots,N$, respectively, and let $X=X_1\cdots X_M$ and $Y=Y_1\cdots Y_N$.…
The Conway-Maxwell-Poisson distribution is a two-parameter generalisation of the Poisson distribution that can be used to model data that is under- or over-dispersed relative to the Poisson distribution. The normalizing constant…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$,…
The Lambert W function gives the solutions of a simple exponential polynomial. The generalized Lambert W function was defined by Mez\"{o} and Baricz, and has found applications in delay differential equations and physics. In this article we…
Asymptotic formulae are established for the number of natural numbers $m$ with largest square-free divisor not exceeding $m^{\vartheta}$, for any fixed positive parameter $\vartheta$. Related counting functions are also considered.