| Meaning: |
-
Distribution of a real random variable \(T = d \cdot N\), whereby \(N\)
represents an arbitrarily distributed discrete random variable and \(d\) the
scale factor.
-
Main application is the description of a cell distance in a time slot system
e.g., on an ATM link. In this case \(d\) is the time slot duration.
-
A special case of the compound distribution with a constant "inner
distribution".
|
| Parameters: |
-
scale factor/time slot duration \(d\)
-
discrete distribution \(p_i\) of \(N\) / the number of time slots
|
| PDF: |
\(P(T=t) = f(t) = \sum\limits_{n=0}^{\infty} p_n \cdot \delta (t-nd) \) |
| Expected value: |
\(E[T] = E[N] \cdot d\) |
| Variance: |
\(VAR[T]= VAR[N] \cdot d^2\) |
| Coefficient of variation: |
\(c_T = c_N\) |
| LST: |
\(\phi(s) = H(exp(-sd))\) , if \(H(z)\) represents the generating
function of \(N\) |
| Parser example: |
[...].Distribution = SlottedDistribution
[...].Distribution.SlotDuration = 1.5
[...].Distribution.NoOfSlotsDist = Geometric
[...].Distribution.NoOfSlotsDist.Mean = 9
|