Gamma Distribution

A probability distribution \(Gamma(k, \lambda)\) having the PDF
\[ \gamma_{k,\lambda}(x) = \frac{\lambda^k x^{k-1} e^{-\lambda x}}{\Gamma(k)} \]
where \(\Gamma(x)\) is the gamma function and that, for integer \(k\), governs the probability of waiting times for \(k\) events that occur at a rate \(\lambda\) and whose arrival is independent of previous arrival times.