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1969•Proceedings of the IEEEOpen access

Approximate calculation of cumulative probability from a moment-generating function

Carl W. Helstrom

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Abstract

A numerical method is presented for calculating the cumulative distribution of a positive random variable from its moment-generating function. It involves an expansion of the rectangular function in Laguerre functions. As examples, the cumulative exponential and cumulative Poisson probability functions are approximated.

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A numerical method is presented for calculating the cumulative distribution of a positive random variable from its moment-generating function. It involves an expansion of the rectangular function in Laguerre functions. As examples, the cumulative exponential and cumulative Poisson probability functions are approximated.

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Available abstract

A numerical method is presented for calculating the cumulative distribution of a positive random variable from its moment-generating function. It involves an expansion of the rectangular function in Laguerre functions. As examples, the cumulative exponential and cumulative Poisson probability functions are approximated.

Key concepts: Cumulative distribution function, Moment-generating function, Mathematics, Moment (physics), Exponential distribution, Laguerre polynomials, Exponential function, Random variable

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