# Weibull distribution

## Calculates the probability density function and lower and upper cumulative distribution functions of the Weibull distribution.

percentile x
 x≧0
shape parameter a
 a＞0
scale parameter b
 b＞0

density f(x,a,b)
lower P(x,a,b)
upper Q(x,a,b)

 $\normal Weibull\ distribution\\[10](1)\ probability\ density\\\hspace{30}f(x,a,b)={\large\frac{a}{b}(\frac{x}{b})^{a-1}e^{-(\frac{x}{b})^a}}\\(2)\ lower\ cumulative\ distribution\\\hspace{30}P(x,a,b)={\large\int_{\small 0}^{\hspace{25pt}\small x}}f(t,a,b)dt={\large 1-e^{-(\frac{x}{b})^a}}\\(3)\ upper\ cumulative\ distribution\\\hspace{30}Q(x,a,b)={\large \int_{\small x}^{\hspace{25}\small\infty}}f(t,a,b)dt={\large e^{-(\frac{x}{b})^a}}\\$

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