Known Weibull shape. For a complete sample of size n from a Weibull distribution with a known shape parameter value ßo and an unknown scale parameter αO, the scale parameter is to be estimated.
(a) Give the sample likelihood function and the log likelihood.
(b) Obtain and solve the likelihood equation for the maximum likelihood estimate & of the scale parameter.
(c) Derive the expression for the sample local Fisher information both in terms of the true value a. of the scale parameter and in terms of the sample estimate.
(d). Derive the expression for the asymptotic Fisher information both in terms of the true value a. of the scale parameter and in terms of the sample estimate & α.
(e)Derive the expressions for the asymptotic variance and standard error for the maximum likelihood estimate h both in terms of the true value a, and the estimate &.
(f) Give expressions for the approximate confidence limits for the true value of the scale parameter-this must be in terms of the estimate ir. (8) Use the results from (b) through (f) and obtain the corresponding sample quantities for the 35-kV data of Table 2.1 of Chapter 7. Assuming.