Q. 5.23 - A First Course in Probability

Question

Compute the hazard rate function of a Weibull random variable and show it is increasing when $𝛽\ge 1$ and decreasing when $𝛽\le 1$

Step-by-Step Solution

Answer

The hazard rate function of Weibul distribution is $H\left(t\right)={\left(𝜆t\right)}^{𝛽}$

Step 1 : Given Information

X  is a Weibull distribution with parameters $𝛌,𝛂 and 𝞫$

Step 2 : Calculations

The hazard function of Weibull function is 

$H\left(t\right)={\left(𝜆t\right)}^{𝛽}$

Step 3 : Plot

In order to better understand we need to see the graph of above function that is

where green graph is for the case when $𝛽\le 1$ and black graph is for the case when $𝛽>0$.

This proves the statement that  hazard rate function of a Weibull random variable and show it is increasing when  and decreasing when