Erlang distribution

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The Erlang distribution is a two-parameter family of continuous probability distributions with support x ∈ [ 0 , ∞ ) {\displaystyle x\in [0,\infty )} . The two parameters are: a positive integer k , {\displaystyle k,} the "shape", and a positive real number λ , {\displaystyle \lambda ,} the "rate". The "scale", β , {\displaystyle \beta ,} the reciprocal of the rate, is sometimes used instead. The Erlang distribution is the distribution of a sum of k {\displaystyle k} independent exponential variables with mean 1 / λ {\displaystyle 1/\lambda } each. Equivalently, it is the distribution of the time until the kth event of a...

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