Question

Discuss the meaning and use of the term beta in the Weibull function.

Answer 1

Answer :

β is the shape parameter in Weibull distribution, it is also known as the Weibull slope. This is because the value of β is equal to the slope of the line in a probability plot. Different values of the shape parameter can have marked effects on the behavior of the distribution. Some values of the shape parameter will cause the distribution equations to reduce to those of other distributions. For example, when β = 1, the pdf of the three-parameter Weibull reduces to that of the two-parameter exponential distribution. The parameter β is a pure number that is it is dimensionless.

The following figure shows the effect of different values of the shape parameter, β, on the shape of the pdf