Suppose that X ~ Gamma(3, b), with pdf f(x|b) = ²e-bz on r> 0, %3D where b> 0. It is required to test the null hypothesis Ho : b= bo against the alternative hypothesis H1 : b= b1, based on a random sample r1,r2, ..., Fn. (a) Find the log-likelihood €(b). (b) Let LR be the likelihood ratio L(b1)/L(bo). Show that the log of the likelihood ratio is
Suppose that X ~ Gamma(3, b), with pdf f(x|b) = ²e-bz on r> 0, %3D where b> 0. It is required to test the null hypothesis Ho : b= bo against the alternative hypothesis H1 : b= b1, based on a random sample r1,r2, ..., Fn. (a) Find the log-likelihood €(b). (b) Let LR be the likelihood ratio L(b1)/L(bo). Show that the log of the likelihood ratio is
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 5SE: What does the y -intercept on the graph of a logistic equation correspond to for a population...
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Transcribed Image Text:Suppose that X ~ Gamma(3, b), with pdf
-br
f(r\b) =
2
on a > 0,
where b> 0. It is required to test the null hypothesis Họ : b= bo against the
alternative hypothesis H1 : b = b1, based on a random sample #1,x2,..., Tn.
(a) Find the log-likelihood l(b).
(b) Let LR be the likelihood ratio L(b1)/L(bo). Show that the log of the
likelihood ratio is
log(LR) = 3n log
bo
(2)
- (b1 – bo) ri-
i=1
(c) Using the expression for log(LR) that you obtained in part (b), show
that the rejection region R= {x : log(LR) > d} for the test is of the
form T< d if b1 > bo. Hence give c' in terms of d.
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