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Generating Random Numbers Based on the Gamma Distribution

TOP/Collection of Applied Calculation Problems/Probability and Statistics
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Generate random numbers based on the gamma distribution.
Shape parameter a
a＞0
Scale parameter b
b＞0
Number of random numbers to generate
(<=1000)
\(\normalsize Gamma\ distribution\\ (1)\ probability\ density\\ \hspace{30px}f(x,a,b)={\large\frac{1}{\Gamma(a)b}(\frac{x}{b})^{a-1}e^{-\frac{x}{b}}}\\ (2)\ lower\ cumulative\ distribution\\ \hspace{30px}P(x,a,b)={\large\int_{\small 0}^{\small x}}f(t,a,b)dt\\ (3)\ upper\ cumulative\ distribution\\ \hspace{30px}Q(x,a,b)={\large\int_{\small x}^{\small\infty}}f(t,a,b)dt\\\)

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