| NestedDistribution |
Nested Distribution
| Meaning:
The nested distribution gives the distribution of a sum of random
variables \(T_1, T_2, ..., T_N\) that each are described by a continuous
("inner") distribution.
|
| PiecewiseLinearDistribution |
Piece-wise Linear Distribution
Piece-wise Linear Distribution
| Meaning:
Distribution of a real random variable \(T = d \cdot (Z + Y)\), whereby
\(Z\) is an arbitrarily distributed integer number random variable, \(Y\) is
an uniformly distributed continuous random variable between 0 and 1 and \(d\)
is the scale factor.
|
| SlottedDistribution |
Continuous Distribution with a Discrete Value Range
| 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.
|
| TransformedDistribution |
Linear Transformed Continuous Distribution
| Meaning:
Distribution of a random variable \(T\), that results from a linear
transformation \(T = aZ + b\) of the random variable \(Z\) with a given
continuous distribution ("base distribution").
| Parameters:
base distribution with PDF \(g(t)\) and DF \(G(t)\)
factor \(a \neq 0\)
offset \(b\)
| PDF:
\(P(T=t) = f(t) = g(\frac{t-b}{a})\)
| DF:
\(P(T \le t) = F(t) = G(\frac{t-b}{a})\)
| Expected value:
\(E[T] = a \cdot E[Z] +b\)
| Variance:
\(VAR[T]= a^2 \cdot VAR[Z]\)
| Coefficient of variation:
\(c_T = \frac{1}{\frac{1}{c_z} + \frac{b}{a \sqrt{VAR[Z]}}}\)
| Parser example:
[...].Distribution = TransformedDistribution
[...].Distribution.BaseDist = NegExp
[...].Distribution.BaseDist.Mean = 2.5
[...].Distribution.Factor = 2.0 # optional, default = 1
[...].Distribution.Offset = 10.0 # optional, default = 0
|
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