Search results for " gamma distribution"
showing 7 items of 7 documents
Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions
2022
Quick detection of an assignable cause is necessary for process accuracy with respect to the specifications. The aim of this study is to monitor the time and magnitude processes based on unit-interval data. To this end, maximum exponentially weighted moving average (Max-EWMA) control chart for simultaneous monitoring time and magnitude of an event is proposed. To be precise, beta and unit gamma distributions are considered to develop the Max-EWMA chart. The chart’s performance is accessed using average run length (ARL), the standard deviation of run length (SDRL), and different quantiles of the run length distribution through extensive Monte Carlo simulations. Besides a comprehensive simula…
On the world distribution of income
2015
In this paper we demonstrate that the size distribution of the world income may be reasonably approximated by a log-normal distribution rather then by a power law, as has previously been believed. This result has been shown to be quite persistent as we move from 1985 to 2011.
A characterization of the distribution of a weighted sum of gamma variables through multiple hypergeometric functions
2008
Applying the theory on multiple hypergeometric functions, the distribution of a weighted convolution of Gamma variables is characterized through explicit forms for the probability density function, the distribution function and the moments about the origin. The main results unify some previous contributions in the literature on nite convolution of Gamma distributions. We deal with computational aspects that arise from the representations in terms of multiple hypergeometric functions, introducing a new integral representation for the fourth Lauricella function F (n) D and its con uent form (n) 2 , suitable for numerical integration; some graphics of the probability density function and distr…
Second-order interaction in a Trivariate Generalized Gamma Distribution
2004
The concept of second- (and higher-) order interaction is widely used in categorical data analysis, where it proves useful for explaining the interdependence among three (or more) variables. Its use seems to be less common for continuous multivariate distributions, most likely owing to the predominant role of the Multivariate Normal distribution, for which any interaction involving more than two variables is necessarily zero. In this paper we explore the usefulness of a second-order interaction measure for studying the interdependence among three continuous random variables, by applying it to a trivariate Generalized Gamma distribution proposed by Bologna(2000).
Moments for Some Kumaraswamy Generalized Distributions
2014
Explicit expansions for the moments of some Kumaraswamy generalized (Kw-G) distributions (Cordeiro and de Castro, 2011) are derived using special functions. We explore the Kw-normal, Kw-gamma, Kw-beta, Kw-t, and Kw-F distributions. These expressions are given as infinite weighted linear combinations of well-known special functions for which numerical routines are readily available.
The exact distribution of a weighted Convolution of two Gamma distributions
2006
Si considera una rappresentazione della funzione di densit`a di probabilit`a di una Convoluzione ponderata di distribuzioni Gamma, in cui una funzione ipergeometrica confluente descrive come le differenze tra i parametri di scala delle componenti determinino allontanamenti da una densit`a Gamma. Si considera il caso specifico di una convoluzione di due variabili gamma per mostrare, come al vantaggio interpretativo si aggiunga la possibilit`a di derivare in forma esplicita e computazionalmente semplice, espressioni della funzione di ripartizione e dei momenti. Si mostra la relazione tra tale distribuzione ed il sistema delle distribuzioni di Bessel, e si generalizza inoltre al caso di convol…
A statistical model for magnitudes and angles of wavelet frame coefficients and its application to texture retrieval
2014
Abstract This paper presents a texture descriptor based on wavelet frame transforms. At each position in the image, and for each resolution level, we consider both vertical and horizontal wavelet detail coefficients as the components of a bivariate random vector. The magnitudes and angles of these vectors are computed. At each level the empirical histogram of magnitudes is modeled by a Generalized Gamma distribution, and the empirical histogram of angles is modeled by a different version of the von Mises distribution that accounts for histograms with 2 modes. Each texture is characterized by few parameters. A new distance is presented (based on the Kullback–Leibler divergence) that allows g…