The reliability of an electrical power system in Iraq was analyzed in the journal PLoS ONE (Aug. 2013). The failure time distribution, f(t), followed a Dagum probability distribution with parameters β, α, and k. The density function takes the form:

The researchers showed that the reliability function for this distribution is:

a. Show that the hazard rate for this distribution is

b. The best fitting distribution for the time between failures of the electrical power system had parameter values β = 90, α = 2.4, and k = .34. Use these values to find and interpret the hazard rate for this failure time distribution.

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%3D ка(1 + B>0, a -0, к > 0 f(1)