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References in periodicals archive ?
Examples of the distribution of W, together with the corresponding cumulant generating function, and the third and fourth cumulants.
As the cumulant generating function of [[??].sub.n] - Q has a simple form, its cumulants are easily available.
For a given kernel function k, we have a simple expression for the cumulant generating function of X and its derivatives (when they exist), cf.
Exponential titling for density approximation introduced by Esscher (1932) provides, a means for creating a regular exponential family from a distribution whose cumulant generating function converges in the regular sense.
Define the cumulant generating function of sample mean [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The cumulant generating function of a Tweedie distribution for 1 < p < 2 is
By comparing the cumulant generating functions in Lemma 1 and Proposition 5 the compound Poisson process can be thought of as Tweedie distribution with parameters ([lambda], [alpha], P) expressed as follows: