Use the failure data in Example 4.19 to obtain the parameter of the failure time distribution when the prior model of the parameter θ follows an exponential distribution given by Compare the estimated...

Use the failure data in Example 4.19 to obtain the parameter of the failure time distribution when the prior model of the parameter θ follows an exponential distribution given by

Compare the estimated value with that of the example. Explain why they are different.

1. Develop an algorithm to obtain random failure times from a two-parameter exponential distribution using the inverse transformation approach. The p.d.f. of the distribution is

Verify the exactness of the variates.

Q337

The following failure times follow a Gamma distribution of the form

where λ is the scale parameter and α is the shape parameter.

(a) Use the MLE method to obtain λ.

(b) Use the value obtained in (a) and the method of moment to obtain α.

(c) What is the MMTF?

(d) What are the characteristics of the hazard function?

(e) Use the bootstrap method to obtain the 95% confidence intervals for both parameters as well as the estimate of their variances.