I'd like to model proportion of certain species in a popualtion with Borel-Tanner distribution: $\frac{e^{-m}m^{m-1}}{m!}$, its support is defined on $\{1,2,...\}$, but I need finite bound. Could anyone help me with finding the finite sum $\sum_{m=1}^{n}\frac{e^{-m}m^{m-1}}{m!}$?
Borel-Tanner distribution with finite bound
1
$\begingroup$
probability-distributions
-
0The Borel-Tanner distribution is not given by the formula you write. Furthermore the sum of the series of general term $\mathrm{e}^{-m}m^m/m!$ is infinite and in particular, not $1$. – 2011-05-21
-
0I edited it accordingly – 2011-05-22
-
0If the (modified) weights you consider sum to $1$, you could show why. – 2011-05-22
-
0I need the sum $\sum_{m=1}^{\mu} \frac{e^{-m}m^{m-1}}{m!}$, and I haven't found it so far – 2011-05-24