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A NOTE ON THE GAMMA DISTRIBUTION
, 1958
"... The general properties of the gamma distribution, which has several applications in meteorology, are discussed. A short review of the general properties of good statistical estimators is given. This is applied to the gamma distribution to show that the maximum likelihood estimators are jointly suffi ..."
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The general properties of the gamma distribution, which has several applications in meteorology, are discussed. A short review of the general properties of good statistical estimators is given. This is applied to the gamma distribution to show that the maximum likelihood estimators are jointly
Estimating a Gamma distribution
, 2002
"... This note derives a fast algorithm for maximumlikelihood estimation of both parameters of a Gamma distribution or negativebinomial distribution. 1 ..."
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Cited by 4 (0 self)
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This note derives a fast algorithm for maximumlikelihood estimation of both parameters of a Gamma distribution or negativebinomial distribution. 1
Abstract Gamma Distribution and Gamma Approximation
"... The Gamma distribution and related approximation properties of this distribution to certain of classes of functions are discussed. Two asymptotic estimate formulas are given. ..."
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The Gamma distribution and related approximation properties of this distribution to certain of classes of functions are discussed. Two asymptotic estimate formulas are given.
QUANTIZERS FOR SYMMETRIC GAMMA DISTRIBUTIONS
"... This paper discussea minimum meansqaare error quantiration for symmetric distributions. If the distribution satisfies a logconcavity condition, the optimal quantirer is itself symmetric. For the gamma distribution ofien used to model speech signals, the logconcavity condition is not satisfied. It ..."
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This paper discussea minimum meansqaare error quantiration for symmetric distributions. If the distribution satisfies a logconcavity condition, the optimal quantirer is itself symmetric. For the gamma distribution ofien used to model speech signals, the logconcavity condition is not satisfied
Convexity of the median in the gamma distribution
, 2006
"... We show that the median m(x) in the gamma distribution with parameter x is a strictly convex function on the positive halfline. 2000 Mathematics Subject Classification: primary 60E05; secondary 41A60, 33B15. ..."
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We show that the median m(x) in the gamma distribution with parameter x is a strictly convex function on the positive halfline. 2000 Mathematics Subject Classification: primary 60E05; secondary 41A60, 33B15.
A GammaDistributed Stochastic Frontier Model
 Journal of Econometrics
, 1990
"... We modify the stochastic frontier model of Aigner, Loveil, and Schmidt to allow the onesided part of the disturbance to have a twoparameter Gamma distribution rather than the less flexible halfnormal distribution. Maximumlikelihood estimation and the estimation of firmspecific ine~ciency estima ..."
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Cited by 123 (4 self)
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We modify the stochastic frontier model of Aigner, Loveil, and Schmidt to allow the onesided part of the disturbance to have a twoparameter Gamma distribution rather than the less flexible halfnormal distribution. Maximumlikelihood estimation and the estimation of firmspecific ine
Maximum Likelihood Phylogenetic Estimation from DNA Sequences with Variable Rates over Sites: Approximate Methods
 J. Mol. Evol
, 1994
"... Two approximate methods are proposed for maximum likelihood phylogenetic estimation, which allow variable rates of substitution across nucleotide sites. Three data sets with quite different characteristics were analyzed to examine empirically the performance of these methods. The first, called ..."
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Cited by 540 (28 self)
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the "discrete gamma model," uses several categories of rates to approximate the gamma distribution, with equal probability for each category. The mean of each category is used to represent all the rates falling in the category. The performance of this method is found to be quite good
BIVARIATE GAMMA DISTRIBUTION AS A LIFE TEST MODEL
, 1982
"... Bivariate gamma distribution as a life test model ..."
PAML: a program package for phylogenetic analysis by maximum likelihood
 COMPUT APPL BIOSCI 13:555–556
, 1997
"... PAML, currently in version 1.2, is a package of programs for phylogenetic analyses of DNA and protein sequences using the method of maximum likelihood (ML). The programs can be used for (i) maximum likelihood estimation of evolutionary parameters such as branch lengths in a phylogenetic tree, the tr ..."
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Cited by 1403 (16 self)
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, the transition/transversion rate ratio, the shape parameter of the gamma distribution for variable evolutionary rates at sites, and rate parameters for different genes; (ii) likelihood ratio test of hypotheses concerning sequence evolution, such as rate constancy and independence among sites and rate constancy
Powerlaw distributions in empirical data
 ISSN 00361445. doi: 10.1137/ 070710111. URL http://dx.doi.org/10.1137/070710111
, 2009
"... Powerlaw distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and manmade phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the t ..."
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Cited by 589 (7 self)
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Powerlaw distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and manmade phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur
Results 1  10
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320,393