Consider the Gamma distribution, with parameters α and λ. Compute the hazard function of a Gamma random variable and show that this hazard function is increasing when α ≥1, and decreasing when α ≤1.

Consider the Gamma distribution, with parameters α and λ. Compute the hazard function of a Gamma random variable and show that this hazard function is increasing when α ≥1, and decreasing when α ≤1.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 1CR

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Question

100%

Consider the Gamma distribution, with parameters α and λ.

Compute the hazard function of a Gamma random variable and show that this hazard
function is increasing when α ≥1, and decreasing when α ≤1.
(Hint: there is nota “nice” closed form for the hazard rate function.)

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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