Weibull Distribution

 

The Type-III asymptotic distribution of the minimum value, developed by Weibull for studying the fatigue and fracture of materials, is known as the Weibull distribution. The two-parameter form is widely used in the life estimation of mechanical and electronic components. It can be represented by setting ε to be zero in the Type-III minimum value distribution is Extreme Value Distribution Value. The CDF of the two-parameter Weibull distribution is

 

The corresponding PDF is

 

For the two-parameter Weibull distribution, the mean and the coefficient of variance are related to the parameters  and  as follows:

 

and

 

If the mean and coefficient of variance are known, the parameters  and  can be approximated for practical applications:

 

and