Question

Present a real life problem that can be formulated by applying the following:

Use of a Hierarchical model, which includes Exponential and Poisson distributions.

Answer 1

define

X: number of egges laid by a species of insect

Y: variability across different mother insects of the species

where X|Y ~ Poisson(lambda)

and lambda ~ Exponential(beta)

then Y ~ Negative Binomial (r=1, p=beta/(1+beta))

[ another example :

we know that a Gamma distribution with shape parameter alpha=1 and scale parameter= beta is equivalent to exponential (beta) distribution.

suppose

accident proneness by a person is defined by Y and Y ~ Gamma(alpha,beta)

if alpha=1

then Y ~ exponential(beta)

X : number of accidents occurred

X|Y defines X accidents occured given accident proneness Y

X|Y ~ Poisson (y)

then X ~ Negative Binomial (r=alpha=1,p=beta/(1+beta)) ]

[ check :

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