## Tuesday, May 20, 2008

### [MT 8] Comments to [MT 7]

Assume again we have a Poisson train of assembly steps (AS) with average number k_av=10 per measurement time intervall. Let each FU require m=2 of the AS. Mentally, we can definde a super-Poisson process, where each pair of AS is merged to a FU-super-unit. Then one might naively think that

P(12,10)=P(having 12 AS done when there would normally be only 10)

might be the same as

P(6,5)=P(having 6 FU done when there would normally be only 5).

However, the Poisson distribution has no such scaling property:

P(12,10)=0.09478033009, but
P( 6, 5)=0.1462228081.

Thus, in general, P( k / m, k_av / m ) is not equal to P( k, k_av ), and the super-Poisson distribution P(n | m, k_av = R dt) defined in [MT 7] is not just a rescaled Poisson distribution.

Note also that the super-Poisson distribution has one extra parameter, m, which brings more flexibility in fitting the experimental SWDs.