Density and distribution evaluation for convolution of independent gamma variables

Chaoran Hu (), Vladimir Pozdnyakov and Jun Yan
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Chaoran Hu: University of Connecticut
Vladimir Pozdnyakov: University of Connecticut
Jun Yan: University of Connecticut

Computational Statistics, 2020, vol. 35, issue 1, No 19, 327-342

Abstract: Abstract Convolutions of independent gamma variables are encountered in many applications such as insurance, reliability, and network engineering. Accurate and fast evaluations of their density and distribution functions are critical for such applications, but no open source, user-friendly software implementation has been available. We review several numerical evaluations of the density and distribution of convolution of independent gamma variables and compare them with respect to their accuracy and speed. The methods that are based on the Kummer confluent hypergeometric function are computationally most efficient. The benefit of employing the confluent hypergeometric function is further demonstrated by a renewal process application, where the gamma variables in the convolution are Erlang variables. We derive a new computationally efficient formula for the probability mass function of the number of renewals by a given time. An R package coga provides efficient C++ based implementations of the discussed methods and are available in CRAN.

Keywords: Confluent hypergeometric function; Distribution theory; Statistical computing; Renewal process (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00180-019-00924-9

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