Aryal, Gokarna, Nadarajah, Saralees (2004)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 33C90, 62E99. The Fisher information matrix for three generalized beta distributions are derived.
Daniel Hlubinka (2003)
Mathematica Bohemica
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The prediction of size extremes in Wicksell’s corpuscle problem with oblate spheroids is considered. Three-dimensional particles are represented by their planar sections (profiles) and the problem is to predict their extremal size under the assumption of a constant shape factor. The stability of the domain of attraction of the size extremes is proved under the tail equivalence condition. A simple procedure is proposed of evaluating the normalizing constants from the tail behaviour of...
Baricz, Árpád (2008)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Gao, Xin, Xu, Hong, Ye, Dong (2009)
International Journal of Mathematics and Mathematical Sciences
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Peter Harremoës (2016)
Kybernetika
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In this paper we derive various bounds on tail probabilities of distributions for which the generated exponential family has a linear or quadratic variance function. The main result is an inequality relating the signed log-likelihood of a negative binomial distribution with the signed log-likelihood of a Gamma distribution. This bound leads to a new bound on the signed log-likelihood of a binomial distribution compared with a Poisson distribution that can be used to prove an intersection...
Nagar, D.K., Jain, S.K., Gupta, A.K. (1985)
International Journal of Mathematics and Mathematical Sciences
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Nadarajah, Saralees (2002)
Serdica Mathematical Journal
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In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr(X2 < X1 ) when X1 and X2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R = Pr(X2 < X1 ) has been worked out for the majority of the well-known distributions including Normal, uniform, exponential, gamma, weibull and pareto. However, there are still many other distributions for which the form...
Christopher S. Withers, Saralees Nadarajah (2011)
Applicationes Mathematicae
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The five-parameter generalized gamma distribution is one of the most flexible distributions in statistics. In this note, for the first time, we provide asymptotic covariances for the parameters using both the method of maximum likelihood and the method of moments.
Knessl, Charles, Szpankowski, Wojciech (2000)
The Electronic Journal of Combinatorics [electronic only]
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Daniel Hlubinka, Samuel Kotz (2010)
Applications of Mathematics
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The generalized FGM distribution and related copulas are used as bivariate models for the distribution of spheroidal characteristics. It is shown that this model is suitable for the study of extremes of the 3D spheroidal particles observed in terms of their random planar sections.