f(y0) = 30 y² exp{-0y³} provided y ≥0 where > 0 is a parameter. (a) Verify that f(y) belongs to an exponential family in canonical form. (b) Determine the maximum likelihood estimator of by solving the generalized moment equations as discussed in our coure notes titled Exponential Families and Maximum Likelihood Estimation.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 18E
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Suppose that Y1, . . . , Yn is a random sample from a population whose density function is

 

f (y\0) = 30 y² exp{-0 y³}
provided y 2 0 where 0 > 0 is a parameter.
(a) Verify that f(y|0) belongs to an exponential family in canonical form.
(b) Determine the maximum likelihood estimator of 0 by solving the generalized moment
equations as discussed in our coure notes titled Exponential Families and Maximum
Likelihood Estimation.
Transcribed Image Text:f (y\0) = 30 y² exp{-0 y³} provided y 2 0 where 0 > 0 is a parameter. (a) Verify that f(y|0) belongs to an exponential family in canonical form. (b) Determine the maximum likelihood estimator of 0 by solving the generalized moment equations as discussed in our coure notes titled Exponential Families and Maximum Likelihood Estimation.
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