EXCERSICE 3. Let X1,..., Xn be iid observations from a location-scale family. Let T1(X1,...,Xn) and T2(X1,..., Xn) be two statistics that both satisfy T:(axı + b, ..., axn + b) = aT:(I1,..., In) for all values of x1,..., In and b and for any a > 0. (a) Show that T1/T2 is an ancillary statistic. (b) Let R be the sample range and S be the sample standard deviation. Verify that R and S satisfy the above condition so that R/S is an ancillary statistic. Dr. Asieh Abtahi - Faculty of Mathematics and Statistics - Islamic Azad University of Shiraz - Iran 13
EXCERSICE 3. Let X1,..., Xn be iid observations from a location-scale family. Let T1(X1,...,Xn) and T2(X1,..., Xn) be two statistics that both satisfy T:(axı + b, ..., axn + b) = aT:(I1,..., In) for all values of x1,..., In and b and for any a > 0. (a) Show that T1/T2 is an ancillary statistic. (b) Let R be the sample range and S be the sample standard deviation. Verify that R and S satisfy the above condition so that R/S is an ancillary statistic. Dr. Asieh Abtahi - Faculty of Mathematics and Statistics - Islamic Azad University of Shiraz - Iran 13
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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
Transcribed Image Text:EXCERSICE e
3
Let X1,..., Xn be iid observations from a location-scale family. Let Ti(X1,...,Xn)
and T2(X1,... , Xn) be two statistics that both satisfy
T:(axı + b, ..., axn + b) = aT:(I1,..., In)
for all values of r1,..., n and b and for any a > 0.
(a) Show that T1/T2 is an ancillary statistic.
(b) Let R be the sample range and S be the sample standard deviation. Verify that
R and S satisfy the above condition so that R/S is an ancillary statistic.
Dr. Asieh Abtahi - Faculty of Mathematics and Statistics -
Islamic Azad University of Shiraz - Iran
13
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