Some results on the ageing class

Leszek Knopik

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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.

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Some properties and applications of probability distributions based on MacDonald function

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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 $x^{n} K_{n} (x), x \geq 0, {|x|}^{n} K_{n} (x |x|), x \in 𝐑$ and $x^{n + 1} K_{n} (x), x \geq 0$ 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...