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The probability density function (also called the Probability Density Function) of a continuous distribution is
defined as the derivative of the (cumulative) Distribution Function
,
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(1) |
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(2) |
A probability density function satisfies
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(3) |
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(4) |
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(5) |
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(6) |
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(7) |
If and
, then
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(8) |
Given the Moments of a distribution (,
, and the Gamma Statistics
), the asymptotic probability function is given by
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(9) |
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(10) |
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(11) |
See also Continuous Distribution, Cornish-Fisher Asymptotic Expansion, Discrete Distribution, Distribution Function, Joint Distribution Function
References
Abramowitz, M. and Stegun, C. A. (Eds.). ``Probability Functions.'' Ch. 26 in
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, pp. 925-964, 1972.
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© 1996-9 Eric W. Weisstein