Consider two independent random samples x_(1),x_(2),dots,x_(n) and Y_(1),Y_(2),dots,Y_(n) taken from \Gamma (k,\lambda _(1)) and \Gamma (k,\lambda _(2)), re- spectively, where \lambda _(1) and \lambda _(2) are the scale parameters for the dis- tributions. Assume that k is known. Show that the lower and upper limits of the confidence interval of (\lambda _(1))\ (\lambda _(2)) interval can be expressed as functions of the quantiles of the F distribution.
Consider two independent random samples x_(1),x_(2),dots,x_(n) and Y_(1),Y_(2),dots,Y_(n) taken from \Gamma (k,\lambda _(1)) and \Gamma (k,\lambda _(2)), re- spectively, where \lambda _(1) and \lambda _(2) are the scale parameters for the dis- tributions. Assume that k is known. Show that the lower and upper limits of the confidence interval of (\lambda _(1))\ (\lambda _(2)) interval can be expressed as functions of the quantiles of the F distribution.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider two independent random samples x_(1),x_(2),dots,x_(n) and
Y_(1),Y_(2),dots,Y_(n) taken from \Gamma (k,\lambda _(1)) and \Gamma (k,\lambda _(2)), re-
spectively, where \lambda _(1) and \lambda _(2) are the scale parameters for the dis-
tributions. Assume that k is known.
Show that the lower and upper limits of the confidence interval of (\lambda _(1))\ (\lambda _(2))
interval can be expressed as
F distribution.
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