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The Generalized Random Variable Appears the Trace of Fractional Calculus in Statistics |
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PP: 61-67 |
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Author(s) |
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Masoud Ganji,
Fatemeh Gharari,
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Abstract |
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| In this paper, introducing a generalized random variable, we obtained a new relationship between fractional calculus and
statistics. With this definition, the domain of shape parameter space for some of distributions, such as Gamma, Beta and Weibull, were
expanded from (0,¥) to (−1,¥). It is shown that the expectation of such random variable ,Fa (x), coincides with the fractional integral
of probability density function (PDF), at the origin, for a > 0, and also the fractional derivative of PDF, at the origin, for −1
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