# Package ikr.simlib.distributions.continuous.transform

• Class Summary
Class Description
BoundedDistribution
Continuous Bounded Distribution
Meaning: Continuous distribution of a random varaible $$T$$ that is bounded between a lower bound and an upper bound.
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