Change of variables: Let = g(), where g is a monotone function of , and let
Fantastic news! We've Found the answer you've been seeking!
Question:
Change of variables: Let ψ = g(θ), where g is a monotone function of θ, and let h be the inverse of g so that θψ = h(ψ). If p θ (θ) is the probability density of θ, then the probability density of ψ induced by Po is given by P ψ (ψ) = P θ (h(ψ)) x |dh/dψ|
(a) Let θ ∼ beta(a, b) and let ψ = log[θ/(1 – θ)]. Obtain the form of p ψ and plot it for the case that a = b = 1.
(b) Let θ ∼ gamma (a, b) and let ψ = log θ. Obtain the form of p ψ and plot it for the case that a = b =1.
Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
Posted Date: