## Two-parameter Weibull Distribution

The probability density function of two parameter Weibull distribution is $$\begin{equation*} f(x)=\left\{ \begin{array}{ll} \frac{\alpha}{\beta} \big(\frac{x}{\beta}\big)^{\alpha-1}e^{-\big(\frac{x}{\beta}\big)^\alpha}, & \hbox{x>0, \alpha, \beta>0;} \\ 0, & \hbox{Otherwise.} \end{array} \right. \end{equation*}$$

• $\alpha$ is the shape parameter
• $\beta$ is the scale parameter

## Mean of Two-parameter Weibull Distribution

The mean of Two-parameter Weibull distribution is

## Variance of Two-parameter Weibull Distribution

The variance of Two-parameter Weibull distribution is

## Distribution function of Weibull Distribution

The distribution function of Three-parameter Weibull distribution is

## Median of Weibull Distribution

The median of two parameter Weibull distribution is