Consider a distribution for which the p.d.f. or the p.f. is f(x|), where the parameter is
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Here, a and c1, . . . , ck are arbitrary functions of θ, and b and d1, . . . , dk are arbitrary functions of x. Suppose now that X1, . . . , Xn form a random sample from a distribution which belongs to a k-parameter exponential family of this type, and define the k statistics T1, . . . , Tk as follows:
Show that the statistics T1, . . . , Tk are jointly sufficient statistics for θ.
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Related Book For
Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
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