The Real Powers of the Convolution of a Gamma Distribution and a Bernoulli Distribution

In this paper, we essentially compute the set of $x,y>0$ such that the mapping z \longmapsto \Big{(}1-r+r e^z\Big{)}^x \Big{(}\dis\frac{\lambda}{\lambda-z}\Big{)}^{y} is a Laplace transform. If $X$ and $Y$ are two independent random variables which have respectively Bernoulli and Gamma distributions, we denote by $\mu$ the distribution of $X+Y.$ The above problem is equivalent to finding the set of $x>0$ such that $\mu^{{\ast}x}$ exists.Comment: Please, i would submit our paper to math arxi

SV MIXTURE, CLASSIFICATION USING EM ALGORITHM

ABSTRACT The present paper presents a theoretical extension of our earlier work entitled"A comparative study of two models SV with MCMC algorithm" cited, Rev Quant Finan Acc (2012

Conditional natural exponential families

Let F={P[theta];[theta][set membership, variant][Theta]} be a natural exponential family on and let H be an exposed face of the closed convex hull of the F support. The aim of this paper is to study the asymptotic behavior of the law P[theta]+[lambda]u as [lambda] increases to +[infinity], for all u exterior normal vector of H. We obtain a degenerate weak limit P[theta],+[infinity] concentrated on the face H. The relation between the conditional law of P[theta] given H and P[theta],+[infinity] is established and some illustrating examples are given.Conditional law Convex Exponential family Face Means domain Variance function

Characterization of multinomial exponential families by generalized variance

In this paper, we show that the multinomial exponential families in a d-dimensional linear space are characterized by the determinant of their covariance matrix, named generalized variance.Exponential family Generalized variance Means domain Multinomial distribution Variance function

Modeling Real-life Data Sets with a Novel G Family of Continuous Probability Distributions: Statistical Properties, and Copulas

This work presents a novel two-parameter G family of continuous probability distributions with compounded parameters. To determine and examine the pertinent mathematical properties, calculations are performed. In one of the special sections, the standard inverse-Rayleigh baseline model is mathematically and statistically emphasized. We generated a number of bivariate and multivariate distributions using the copula method. These new distributions will aid in the modelling of bivariate and multivariate data. The applicability and flexibility of the new compounded two-parameters-G family are demonstrated through three applications to real-life data sets. These examples demonstrate the applicability of the family

The mean radius of curvature of an exponential family

Let F=F([mu]) be the natural exponential family (NEF) on the Euclidean space generated by the measure [mu] and let k[mu]=log L[mu] be the log-Laplace transform of [mu]. In this paper, a notion of mean radius of curvature function for the NEF F is introduced using the mean radius of curvature function of the convex epigraph of the function k[mu]. An algebraic property for the variance function of F is deduced and some characteristic properties for the family F related to the mean radius of curvature function are discussed. The results are illustrated by some examples.Exponential family Variance function Support function

Implicit parameter estimation for conditional gaussian bayesian networks

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