APPROXIMATING PROBABILITY DISTRIBUTION FUNCTIONS WITH FEW MOMENTS
DOI:
https://doi.org/10.52292/j.laar.2020.132Keywords:
Moment problem, Sum of RVs, Product of RVs, Piecewise linear functions, Five-parameter logistic functionAbstract
A procedure is presented for approximating a given probability distribution function
or statistical data considering a subset of their moments.
This is done by a method of fitting moments of a piecewise linear function
to the moments of the known data. The approach has many advantages over popular approximation approaches.
The procedure is demonstrated with commonly used cdfs (Exponential, Gamma, Log-Normal, Normal) and
more difficult problems involving sum and product of random variables,
obtaining good agreement between the theoretical/simulation curves and the piecewise linear approximations.
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