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

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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.

1.3043 1.0878 0.33453 0.49254 1.9461 1.1227 1.2742 0.47615 2.0296 1.4019 3.6454 1.2797 0.32556 0.15344 0.96080 0.29965 1.2357 2.0070 0.26423 0.96381