May 1, 2021, Revision: 1.3

Erlang distribution

f(x) = \frac{λ^{k}x^{k−1}e^{−λx}}{(k − 1)!}  (1)

The two tables below give the skewness and the kurtosis of the Erlang distribution for k = 1, 2, ..., 10 and either λ = 1 or 10. The skewness is always negative, except for k = 1, while in our models it is always positive. The kurtosis is always positive, in agreement with our models, but is always larger than the largest values in our models.

k   skew   kurt  for (lam=1)
1   0.21  -0.96
2  -1.01   1.51
3  -0.79   1.18
4  -0.65   0.76
5  -0.61   0.56
6  -0.63   0.49
7  -0.70   0.52
8  -0.80   0.65
9  -0.92   0.87
10  -1.03   1.16
k   skew   kurt  for (lam=10)
lam = 10
1   0.34  -0.80
2  -0.72   0.36
3  -0.77   1.09
4  -0.62   0.76
5  -0.53   0.56
6  -0.47   0.44
7  -0.42   0.36
8  -0.39   0.31
9  -0.36   0.27
10  -0.34   0.23

$Header: /srv/cvs/brandenb/tex/xiangyu/lucky/idl/erlang/notes.tex,v 1.3 2021/05/01 08:05:51 cvs Exp $

Figure 1: λ = 1, k = 1, 2, ..., 10. All curves for k = 1 are flat for small x.

Figure 2: λ = 10, k = 1, 2, ..., 10. All curves for k = 1 are flat for small x.