Concept explainers
A member of the Pareto family of distributions (often used in economics to model income distributions) has a distribution
where α, β > 0.
a Find the density function.
b For fixed values of β and α, find a transformation G(U) so that G(U) has a distribution function of F when U has a uniform distribution on the interval (0, 1).
c Given that a random sample of size 5 from a uniform distribution on the interval (0, 1) yielded the values .0058, .2048, .7692, .2475 and .6078, use the transformation derived in part (b) to give values associated with a random variable with a Pareto distribution with α = 2, β = 3.
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Chapter 6 Solutions
Mathematical Statistics with Applications
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