The moments of some random variables can be used to specify their distributions, via their moment generating functions.
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The characteristic function and moment generating function of 3-parameter Weibull distribution have also been derived by by a direct approach.
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The fact that there is a simple expression for the moment generating function implies that simple expressions for all moments are available.
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For an Hermite distribution with parameters " X " 1 and " X " 2, the moment generating function exists and is equal to
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Since the chi-squared is in the family of gamma distributions, this can be derived by substituting appropriate values in the moment generating function of the sufficient statistic.
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Which diverges for t > 0 and is therefore not defined in an interval around zero, so that the moment generating function is not defined " per se ".
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Since the moment generating function M _ X ( \ alpha; \ beta; \ cdot ) has a positive radius of convergence, the beta distribution is determined by its moments.
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:: Create a page called'log moment generating function'or whatever and put the following on it " # REDIRECT Cumulant generating function " See WP : R for more.
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The equation for the moment of any integer order of the fractional Poisson can be easily found by means of the moment generating function H _ \ mu ( s, t ) which is defined as
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*PM : moment generating function of the sum of independent random variables, id = 9628 new !-- WP guess : moment generating function of the sum of independent random variables-- Status:
