Show that if g(x) sinh 1 (x) then Deduce that if x NB(n,) has a negative binomial distribution of index n and parameter and z g(x) then Ez sinh 1 (x) and Vz 1 4n What does this suggest as a reference prior for g'(x) n (x n) 1 (x n) ...

Lets start by finding the derivative of gx sinh The inverse hyperbolic sine function sinh u is defin ...

Show that if g(x) = sinh - 1 (x) then Deduce that if x ~ NB(n,) has

Question:

Show that if g(x) = sinh^-¹ √(x) then

g'(x) = {n[(x){1+(x)}].

Deduce that if x ~ NB(n,π) has a negative binomial distribution of index n and parameter π and z = g(x) then Ez ≅ sinh^-1√(x) and Vz ≅ 1/4n. What does this suggest as a reference prior for π ?

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Bayesian Statistics An Introduction

ISBN: 9781118332573

4th Edition

Authors: Peter M. Lee

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Question Posted: Nov 28, 2023 04:32 AM

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Show that if g(x) = sinh - 1 (x) then Deduce that if x ~ NB(n,) has

Question:

g'(x) = {n¯¹[(x/n){1+(x/n)}]¯½.

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Lets start by finding the derivative of gx sinh The inverse hyperbolic sine function sinh u is defin...View the full answer

Bayesian Statistics An Introduction

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