Cornish-fisher Expansions for Poisson and Negative Binomial Processes
نویسندگان
چکیده
Negative binomial and Poisson processes {X(t), t ≥ 0} have cumulants proportional to the rate λ. So, formal Cornish-Fisher expansions in powers of λ−1/2 are available for their cumulative distribution function and quantiles. If T is an independent random variable with cumulants proportional to γ then the cumulants of X(T ) are proportional to γ; so, CornishFisher expansions in powers of γ−1/2 are available for its cumulative distribution function and quantiles. When T has a gamma distribution, alternative expansions in powers of γ−1 are available for the probability mass function of X(T ).
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