8.12. In the zero-inflated Poisson model, random data xi...xn are assumed to be of the form xrii where the y have a Poi(a) distribution and the have a Ber(p) distribution, all independent of each oth...
8.12. In the zero-inflated Poisson model, random data xi...xn are assumed to be of the form xrii where the y have a Poi(a) distribution and the have a Ber(p) distribution, all independent of each other. Given an outcome x-(xi, , X.), the objective is to estimate both λ and p. Consider the following hierarchical Bayesian model: P U(0, 1) alp) Gammala, b) rlp.i)~Ber(p independently (x,lr.λ.Ρ) ~ Poiar.) independently . where r () and a and b are known parameters. We...
3. Let Xi, , Xn be a random sample from a Poisson distribution with p.m.f Assume the prior distribution of Of λ is is an exponential with mean 1, i.e. the prior pdi g(A) e-λ, λ > 0 Note that the exponential distribution is a special gamma distribution; and a general gamma distribution with parameters α > 0 and β > 0 has the pd.f. h(A; α, β)-16(. otherwise Also the mean of a gamma random variable with the pd.f.h(Χα,...
PROBABILITY QUESTION The Poisson distribution is a useful discrete distribution which can be used to model the number of occur rences of something per unit time. If X is Poisson distributed, i.e. X Poisson(λ), its probability mass function takes the following form: oisson distributed, i.e. X - Assume now we have n identically and independently drawn data points from Poisson(A) :D- {r1,...,Xn Question 3.1 [5 pts] Derive an expression for maximum likelihood estimate (MLE) of λ. Question 3.2 5pts Assume...
1. Suppose that Xi,..,Xn are independent Exponential random variables with density f(x; λ) λ exp(-1x) for x > 0 where λ > 0 is an unknown parameter (a) Show that the τ quantile of the Exponential distribution is F-1 (r)--X1 In(1-7) and give an approximation to Var(X(k)) for k/n-T. What happens to this variance as τ moves from 0 to 1? (b) The form of the quantile function in part (a) can be used to give a quantile-quantile (QQ) plot...
1. Suppose that Xi,..,Xn are independent Exponential random variables with density f(x; λ) λ exp(-1x) for x > 0 where λ > 0 is an unknown parameter (a) Show that the τ quantile of the Exponential distribution is F-1 (r)--X1 In(1-7) and give an approximation to Var(X(k)) for k/n-T. What happens to this variance as τ moves from 0 to 1? (b) The form of the quantile function in part (a) can be used to give a quantile-quantile (QQ) plot...