If T is a continuous random variable that is always positive (such as a waiting time), with probability density function f (t) and cumulative distribution function F(t), then the hazard function is defined to be the function The hazard function is the rate of failure per unit time, expressed as a p...

a b Now 0 0 and t 0 so ht 0 if 1 0 and ht 0 if 1 0 Therefore h ...

If T is a continuous random variable that is always positive (such as a waiting time), with

Question:

If T is a continuous random variable that is always positive (such as a waiting time), with probability density function f (t) and cumulative function F(t), then the hazard function is defined to be the function

f (t) h(t) : 1- F(t)

The hazard function is the rate of failure per unit time, expressed as a proportion of the items that have not failed.

a. If T ˆ¼ Weibull (Î±, Î²), find h(t).

b. For what values of Î± is the hazard rate increasing with time? For what values of Î± is it decreasing?

c. If T has an exponential distribution, show that the hazard function is constant.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...

Fantastic news! We've Found the answer you've been seeking!