Let X1,.., Xn, be a random sample from the following probability distribution x+1 fX(x)=0De-*/", x > 0,0 elsewhere and e > 0. (a) Show that f belongs to a regular exponential family. (b) Find a complete sufficient statistics S of 0. (c) Find its expected value and its variance of S.

Let X1,.., Xn, be a random sample from the following probability distribution x+1 fX(x)=0De-*/", x > 0,0 elsewhere and e > 0. (a) Show that f belongs to a regular exponential family. (b) Find a complete sufficient statistics S of 0. (c) Find its expected value and its variance of S.

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Let X1,..., Xn, be a random sample from the following probability distribution
fX(x)=0+1)e
-피/0
I+1
x > 0,0 elsewhere
and e > 0.
(a) Show that f belongs to a regular exponential family.
(b) Find a complete sufficient statistics S of e.
(c) Find its expected value and its variance of S.

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