Let X have the pdf where the distribution of ? is Find the

Chapter 6, Problem 4E

(choose chapter or problem)

Let $X$ have the pdf

$f(x \mid \theta)=\theta \tau x^{\tau-1} e^{-\theta x^{\tau}}, \quad 0<x<\infty$,

where the distribution of $\theta$ is $\Gamma(\alpha, \beta)$. Find the compound distribution of $X$, which is called the Burr distribution.

Equation Transcription:

$X$

$f(x∣\theta{})=\theta{}\tau{}{{x}^{\tau{}-1}e}^{-\theta{}{x}^{\tau{}}},\ \ \ \ 0<x<\infty{}$

$\theta{}$

$\Gamma{}(\alpha{},\beta{})$

Text Transcription:

f(x∣Theta)=Theta tau x^tau-1 e^-theta x^tau, 0<x< infinity

Theta

gamma(alpha,beta)

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