For the hierarchical model YA Poisson (A) and A~ gamma(a, 3) find the marginal distribution, mean, and variance of Y. Show that the margina distribution of Y is a negative binomial if a is an integer.
For the hierarchical model YA Poisson (A) and A~ gamma(a, 3) find the marginal distribution, mean, and variance of Y. Show that the margina distribution of Y is a negative binomial if a is an integer.
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.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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Question
![(a) For the hierarchical model
YA Poisson (A) and
2
A gamma(a, B)
2
find the marginal distribution, mean, and variance of Y. Show that the marginal
distribution of Y is a negative binomial if a is an integer.
(b) Show that the three-stage model
YIN binomial(N, p), NA~ Poisson(A), and
leads to the same marginal (unconditional) distribution of Y.
gamma(a, 3)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33fd386a-3061-4e52-b7a5-fdb411f86070%2F9c0794df-611d-4c94-a0d6-41a98bfe40aa%2Fv3w4uds_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) For the hierarchical model
YA Poisson (A) and
2
A gamma(a, B)
2
find the marginal distribution, mean, and variance of Y. Show that the marginal
distribution of Y is a negative binomial if a is an integer.
(b) Show that the three-stage model
YIN binomial(N, p), NA~ Poisson(A), and
leads to the same marginal (unconditional) distribution of Y.
gamma(a, 3)
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