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Weibull Distribution

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Calculate the probability density function, lower cumulative probability, and upper cumulative probability of the Weibull distribution.
Percentile x
x≧0
Shape parameter a
a＞0
Scale parameter b
b＞0
\(\normalsize Weibull\ distribution\\ (1)\ probability\ density\\ \hspace{30px}f(x,a,b)={\large\frac{a}{b}(\frac{x}{b})^{a-1}e^{-(\frac{x}{b})^a}}\\ (2)\ lower\ cumulative\ distribution\\ \hspace{30px}P(x,a,b)={\large\int_{\small 0}^{\small x}}f(t,a,b)dt={\large 1-e^{-(\frac{x}{b})^a}}\\ (3)\ upper\ cumulative\ distribution\\ \hspace{30px}Q(x,a,b)={\large \int_{\small x}^{\small\infty}}f(t,a,b)dt={\large e^{-(\frac{x}{b})^a}}\\\)

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