Displaying similar documents to “Properties of k-beta function with several 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.

Some monotonicity and limit results for the regularised incomplete gamma function

Wojciech Chojnacki (2008)

Annales Polonici Mathematici

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Letting P(u,x) denote the regularised incomplete gamma function, it is shown that for each α ≥ 0, P(x,x+α) decreases as x increases on the positive real semi-axis, and P(x,x+α) converges to 1/2 as x tends to infinity. The statistical significance of these results is explored.

Successive derivatives and finite expansions involving the H-function of one and more variables

C. M. Joshi, N. L. Joshi (1997)

Annales Polonici Mathematici

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Certain results including the successive derivatives of the H-function of one and more variables are established. These remove the limitations of Ławrynowicz's (1969) formulas and as a result extend the results of Skibiński [13] and various other authors. As an application some finite expansion formulas are also established, which reduce to hypergeometric functions of one and more variables that are of common interest.

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.

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...

Characterizations of inequality orderings by means of dispersive orderings.

Héctor M. Ramos Romero, Miguel Angel Sordo Díaz (2002)

Qüestiió

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The generalized Lorenz order and the absolute Lorenz order are used in economics to compare income distributions in terms of social welfare. In Section 2, we show that these orders are equivalent to two stochastic orders, the concave order and the dilation order, which are used to compare the dispersion of probability distributions. In Section 3, a sufficient condition for the absolute Lorenz order, which is often easy to verify in practice, is presented. This condition is applied in...