Question

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

Short answer

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

Step-by-step solution

Given Information

X is a Weibull distribution with parameters $𝛌,𝛂and𝞫$

Calculations

The hazard function of Weibull function is

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

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 localid="1650453593374" $𝛽>0$.

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