The following data were generated by the Weibull distribution of Exercise 4 a Obtain the maximum likelihood estimates of and , and estimate the asymptotic covariance matrix for the estimates b Carry out a Wald test of the hypothesis that 1 c Obtain the maximum likelihood estimate of under the hypot...

As suggested in the previous problem we can concentrate the log likelihood over From log L 0 we find ...

The following data were generated by the Weibull distribution of Exercise 4: a. Obtain the maximum likelihood

Question:

The following data were generated by the Weibull distribution of Exercise 4:

a. Obtain the maximum likelihood estimates of α and β, and estimate the asymptotic covariance matrix for the estimates.

b. Carry out a Wald test of the hypothesis that β = 1.

c. Obtain the maximum likelihood estimate of α under the hypothesis that β = 1.

d. Using the results of parts a and c, carry out a likelihood ratio test of the hypothesis that β = 1.

e. Carry out a Lagrange multiplier test of the hypothesis that β = 1.

Distribution
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