Let Y₁, Y2,..., Yn be a random sample from the inverse Gaussian distribution with probability density function: 1 F(V. H. 2) = (2²) ²0 ²1 ² { elsewhere if y> 0

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 23E
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Let Y₁, Y₂,..., Yn be a random sample from the inverse Gaussian distribution with
probability density function:
f(y, μ, 2) =
{
Where μ and are unknown.
a) What are
i.
1 -ACT
√
λ
2ny3)že
elsewhere
if y > 0
the likelihood
ii. the log likelihood functions of u and λ.
b) Find the maximum likelihood estimators of u and 2.
Transcribed Image Text:Let Y₁, Y₂,..., Yn be a random sample from the inverse Gaussian distribution with probability density function: f(y, μ, 2) = { Where μ and are unknown. a) What are i. 1 -ACT √ λ 2ny3)že elsewhere if y > 0 the likelihood ii. the log likelihood functions of u and λ. b) Find the maximum likelihood estimators of u and 2.
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