Does this posterior distribution still belong to the Gamma distribution family? If so, what are the parameters?

MATLAB: An Introduction with Applications
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Does this posterior distribution still belong to the Gamma distribution family? If so, what
are the parameters?
Transcribed Image Text:Does this posterior distribution still belong to the Gamma distribution family? If so, what are the parameters?
Suppose we draw an i.i.d. sample X1, ...,X, from a Poisson(1) distribution, where l is a parameter
of unknown value. The pdf of the Poisson(1) distribution is
f(xi)
x;!
Suppose that 2 is treated as a random variable, and the prior distribution for 2 is Gamma, i.c.
1 ~ Gamma(a, B). The prior pdf for 2 is
π(λ)-
- ga-1e-ßA for 1 > 0.
Г(а)
Transcribed Image Text:Suppose we draw an i.i.d. sample X1, ...,X, from a Poisson(1) distribution, where l is a parameter of unknown value. The pdf of the Poisson(1) distribution is f(xi) x;! Suppose that 2 is treated as a random variable, and the prior distribution for 2 is Gamma, i.c. 1 ~ Gamma(a, B). The prior pdf for 2 is π(λ)- - ga-1e-ßA for 1 > 0. Г(а)
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