Statistics for Maintenance Modelling: Continuous Lifetime Distributions 2

# Question to Calculate the Hazard Function for the Gamma Distribution¤

Using Excel, estimate the derivative of the hazard function at t = 4 for the parameter values N = 10 and lambda = 3. Click on one of the options below which approximates the answer, then click on "Check Answer". Click here to launch Excel - if this opens in Internet Explorer, click here.

0.25.
0.36.
0.45.
0.55.
None of these.
Yes, that's right. Evaluating the hazard function at 4, and at a nearby point such as 4.00001, and dividing both by the difference 0.00001 is achieved in Excel by:
((GAMMADIST(4.00001, 10,1/3,FALSE)/(1-GAMMADIST(4.00001, 10,1/3,TRUE)))-(GAMMADIST(4.0, 10,1/3,FALSE)/
(1-GAMMADIST(4.0,10,1/3,TRUE))))/0.00001 0.36.
No, the answer is approximately 0.36. You need to evaluate the hazard function at 4, and at a nearby point such as 4.00001, and divide both by the difference 0.00001. Since and
R(t) = 1 - F(t), this is achieved in Excel by:
((GAMMADIST(4.00001, 10,1/3,FALSE)/(1-GAMMADIST(4.00001, 10,1/3,TRUE)))-(GAMMADIST(4.0, 10,1/3,FALSE)/
(1-GAMMADIST(4.0,10,1/3,TRUE))))/0.00001.