Let X1, ..., X, be a random sample from a gamma distri- bution with parameters a and ß. a. Derive the equations whose solutions yield the maximum likelihood estimators of a and B. Do you think they can be solved explicitly? b. Show that the mle of u = aß is û = X.

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.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Let X1, ..., X, be a random sample from a gamma distri-
bution with parameters a and ß.
a. Derive the equations whose solutions yield the
maximum likelihood estimators of a and B. Do you
think they can be solved explicitly?
b. Show that the mle of u = aß is û = X.
Transcribed Image Text:Let X1, ..., X, be a random sample from a gamma distri- bution with parameters a and ß. a. Derive the equations whose solutions yield the maximum likelihood estimators of a and B. Do you think they can be solved explicitly? b. Show that the mle of u = aß is û = X.
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