Displaying similar documents to “On the ratio of Pearson type VII and Bessel random variables.”

On the ratio of gamma and Rayleigh random variables

Saralees Nadarajah (2007)

Applicationes Mathematicae

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The gamma and Rayleigh distributions are two of the most applied distributions in engineering. Motivated by engineering issues, the exact distribution of the quotient X/Y is derived when X and Y are independent gamma and Rayleigh random variables. Tabulations of the associated percentage points and a computer program for generating them are also given.

Generalized F tests in models with random perturbations: the gamma case

Célia Maria Pinto Nunes, Sandra Maria Bargão Saraiva Ferreira, Dário Jorge da Conceição Ferreira (2009)

Discussiones Mathematicae Probability and Statistics

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Generalized F tests were introduced for linear models by Michalski and Zmyślony (1996, 1999). When the observations are taken in not perfectly standardized conditions the F tests have generalized F distributions with random non-centrality parameters, see Nunes and Mexia (2006). We now study the case of nearly normal perturbations leading to Gamma distributed non-centrality parameters.

Drought models based on Burr XII variables

Saralees Nadarajah, B. M. Golam Kibria (2006)

Applicationes Mathematicae

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Burr distributions are some of the most versatile distributions in statistics. In this paper, a drought application is described by deriving the exact distributions of U = XY and W = X/(X+Y) when X and Y are independent Burr XII random variables. Drought data from the State of Nebraska are used.

Some properties and applications of probability distributions based on MacDonald function

Oldřich Kropáč (1982)

Aplikace matematiky

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In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types x n K n ( x ) , x ≥ 0 , x n K n ( x x ) , x ∈ 𝐑 and x n + 1 K n ( x ) , x ≥ 0 are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and...

Exact and approximate distributions for the product of Dirichlet components

Saralees Nadarajah, Samuel Kotz (2004)

Kybernetika

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It is well known that X / ( X + Y ) has the beta distribution when X and Y follow the Dirichlet distribution. Linear combinations of the form α X + β Y have also been studied in Provost and Cheong [S. B. Provost and Y.-H. Cheong: On the distribution of linear combinations of the components of a Dirichlet random vector. Canad. J. Statist. 28 (2000)]. In this paper, we derive the exact distribution of the product P = X Y (involving the Gauss hypergeometric function) and the corresponding moment properties. We also...