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On the ratio of gamma and Rayleigh random variables

Saralees Nadarajah (2007)

Applicationes Mathematicae

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.

On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function

Kalla, S., Yadav, R., Purohit, S. (2005)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 33D60, 26A33, 33C60The present paper envisages the applications of Riemann-Liouville fractional q-integral operator to a basic analogue of Fox H-function. Results involving the basic hypergeometric functions like Gq(.), Jv(x; q), Yv(x; q),Kv(x; q), Hv(x; q) and various other q-elementary functions associated with the Riemann-Liouville fractional q-integral operator have been deduced as special cases of the main result.

On the use of difference of two proportions

Saralees Nadarajah (2009)

Applicationes Mathematicae

Differences of two proportions occur most frequently in biomedical research. However, as far as published work is concerned, only approximations have been used to study the distribution of such differences. In this note, we derive the exact probability distribution of the difference of two proportions for seven flexible beta type distributions. The expressions involve several well known special functions. The use of these results with respect to known approximations is illustrated.

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