| DiscreteBoundedDistribution |
Discrete Bounded Distribution
| Meaning:
Discrete analogon to the continuous bounded distribution, whereby the
upper and lower limits each belong to the value range of the random variable
\(X\).
| Parameters:
base distribution \(q_i\) with the corresponding DF \(Q_i\)
lower limit \(b_l\) (integer number)
upper limit \(b_u\) (integer number)
boolean value
resampling
Distribution:
\(P(X=i) = p_i = \begin{cases} \frac{q_i}{Q_{b_u}-Q_{b_i}} &\mbox{for }
b_l \le i \le b_u \\ 0 &\mbox{else} \end{cases}\)
| Parser example:
[...].Distribution = DiscreteBoundedDistribution
[...].Distribution.BaseDist = Binomial
[...].Distribution.BaseDist.Mean = 10.0
[...].Distribution.BaseDist.Variance = 5.0
[...].Distribution.LowerBound = 0 # optional, default 0
[...].Distribution.UpperBound = 20 # optional, def.
| DiscreteTransformedDistribution |
Linear Transformed Continuous Distribution
| Meaning:
Distribution of a discrete random variable \(X\), that results from a
linear transformation \(X = aY + b\) of the random variable \(Y\) with a
given discrete distribution ("base distribution").
| Parameters:
base distribution \(q_i\)
integer number factor \(a \neq 0\)
integer number offset \(b\)
Distribution:
\(P(X=i) = p_i = \begin{cases} q_j &\mbox{for } i=aj+b, j=0,1,...
|
| FlooredDistribution |
Floored Distribution
Meaning:
The "floored distribution" is a discrete distribution that converts the
value obtained from a continuous ("base") distribution to an integer value
using the
floor() function from the Java
Math package.
|
| RoundedDistribution |
Rounded Distribution
Meaning:
The "rounded distribution" is a discrete distribution that converts the
value obtained from a continuous ("base") distribution to an integer value
using the
rint() function from the Java
Math package.
|
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