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• W1971066544 abstract "ABSTRACT Though the Pareto distribution is important to actuaries and economists, an exact expression for the distribution of the sum of n i.i.d. Pareto variates has been difficult to obtain in general. This article considers Pareto random variables with common probability density function (pdf) f(x) = (α/β) (1 + x/β)α+1 for x > 0, where α = 1,2,… and β > 0 is a scale parameter. To date, explicit expressions are known only for a few special cases: (i) α = 1 and n = 1,2,3; (ii) 0 < α < 1 and n = 1,2,…; and (iii) 1 < α < 2 and n = 1,2,…. New expressions are provided for the more general case where β > 0, and α and n are positive integers. Laplace transforms and generalized exponential integrals are used to derive these expressions, which involve integrals of real valued functions on the positive real line. An important attribute of these expressions is that the integrands involved are non oscillating." @default.
• W1971066544 created "2016-06-24" @default.
• W1971066544 creator A5007851164 @default.
• W1971066544 date "2006-04-01" @default.
• W1971066544 modified "2023-09-23" @default.
• W1971066544 title "The Distribution of Sums of Certain I.I.D. Pareto Variates" @default.
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• W1971066544 doi "https://doi.org/10.1080/03610920500476325" @default.
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