Insulating  fluid (Weibull). Use the 26-kV data on time to breakdown of an insulating fluid in Table 1.1 of Chapter 3. Use a computer program if you have one.

(a)    Make a Weibull plot of the data, and graphically estimate the Weibull parameters.

(b)   Iteratively solve (3.3) to get the ML estimate of the shape paranieter accurate to two decimal places; use the estimate from (a) to start the iteration.

(c)    Use (3.4) to get the ML estimate of the scale parameter.

(d)   Use (3.1 I) to calculate the sample local Fisher information matrix for the corresponding extreme value parameter estimates.

(e)   Calculate the local estimate of the asymptotic covariance matrix for the ML estimates of the parameters of the corresponding extreme value distribution.

(f)     Calculate two-sided approximate 95% confidence limits for ihe extreme value scale parameter and corresponding limits for the Weibull shape parameter. Are the data consistent with a true shape parameter of I?

(g)    Calculate the ML estimate fur the 10th percentile of the Weibull distribution

(h)   Calculate the local estimate of the asymptotic variance of the ML estimator for the 10th percentile of the corresponding extreme value distribution

(i)      Calculate two-sided approximate 95% confidence limits for the extreme value 10th percentile and corresponding limits for the Weibull 10th percentile

(j)     Calculate exact limits for the parameters and 10th percentile using tables referenced in Section 3.

(k)    

Table 1.1