The Distribution of Sums of I.I.D. Pareto Random Variables with Arbitrary Shape Parameter

Laplace transforms are used to derive an exact expression for the cdf of the sum of n i.i.d. Pareto random variables with common pdf f(x) = (α/β)(1 + x/β) −α−1 for x > 0, where α > 0 and is not an integer, and β > 0. An attractive feature of this expression is that it involves an integral o...

Full description

Saved in:
Bibliographic Details
Published in:Communications in statistics. Theory and methods 2008-05, Vol.37 (14), p.2177-2184
Main Author: Ramsay, Colin M.
Format: Article
Language:English
Subjects:
Distribution theory
Exact sciences and technology
General topics
Incomplete gamma function
Kummer function
Laplace transform
Mathematical analysis
Mathematics
Pareto distribution
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Special functions
Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Laplace transforms are used to derive an exact expression for the cdf of the sum of n i.i.d. Pareto random variables with common pdf f(x) = (α/β)(1 + x/β) −α−1 for x > 0, where α > 0 and is not an integer, and β > 0. An attractive feature of this expression is that it involves an integral of non oscillating real-valued functions on the positive real line. Examples of values of cdfs are provided and are compared to those determined via simulations.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610920701882503