Maurice Tutor

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    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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    Phoniex University
    Oct-2001 - Nov-2016

Category > Management Posted 10 Feb 2018 My Price 9.00

Pareto distribution

Refer to Exercise 9.44. If β is known, show that the Pareto distribution is in the exponential family. What is a sufficient statistic for α? Argue that there is no contradiction between your answer to this exercise and the answer you found in Exercise 9.44.

Exercise 9.44

Let Y1, Y2, . . . , Yn denote independent and identically distributed random variables from a Pareto distribution with parameters α and β. Then, by the result in Exercise 6.18, if α, β > 0,

 

Exercise 6.18

A member of the Pareto family of distributions (often used in economics to model income distributions) has a distribution function given by

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.

 

Answers

Maurice Tutor
(5)
Status NEW Posted 10 Feb 2018 11:02 PM My Price 9.00

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