The probability density function of a known distribution is 1 f(u10) = T O exp (-), y>0, r(v) where I(v) is the Gamma function, and 0, v > 0. (a) Show that this distribution falls within the exponential family given v is known. Specify the components: a(y), b(0), c(0), d(y). (b) Find the mean and variance of this distribution using the expressions obtained in part (a). Results should be given in terms of 0 and v. (c) Point out one practical issue with model fitting when the canonical link function is used.

The probability density function of a known distribution is 1 f(u10) = T O exp (-), y>0, r(v) where I(v) is the Gamma function, and 0, v > 0. (a) Show that this distribution falls within the exponential family given v is known. Specify the components: a(y), b(0), c(0), d(y). (b) Find the mean and variance of this distribution using the expressions obtained in part (a). Results should be given in terms of 0 and v. (c) Point out one practical issue with model fitting when the canonical link function is used.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 29CR

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