naginterfaces.library.rand.dist_​triangular

naginterfaces.library.rand.dist_triangular(n, xmin, xmed, xmax, statecomm)

dist_triangular generates a vector of pseudorandom numbers from a triangular distribution with parameters $x_{min}$, $x_{med}$ and $x_{max}$.

For full information please refer to the NAG Library document for g05sp

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g05/g05spf.html

Parameters

nint

$n$, the number of pseudorandom numbers to be generated.

xminfloat

The end point $x_{min}$ of the triangular distribution.

xmedfloat

The median of the distribution $x_{med}$ (also the location of the vertex of the triangular distribution at which the PDF reaches a maximum).

xmaxfloat

The end point $x_{max}$ of the triangular distribution.

statecommdict, RNG communication object, modified in place

RNG communication structure.

This argument must have been initialized by a prior call to init_repeat() or init_nonrepeat().

Returns

xfloat, ndarray, shape $\left(n\right)$

The $n$ pseudorandom numbers from the specified triangular distribution.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $3$)

On entry, $xmed=⟨value⟩$ and $xmin=⟨value⟩$.

Constraint: $xmed\ge xmin$.

(errno $4$)

On entry, $xmax=⟨value⟩$ and $xmed=⟨value⟩$.

Constraint: $xmax\ge xmed$.

(errno $5$)

On entry, $statecomm$[‘state’] vector has been corrupted or not initialized.

Notes

The triangular distribution has a PDF (probability density function) that is triangular in profile. The base of the triangle ranges from $x=x_{min}$ to $x=x_{max}$ and the PDF has a maximum value of $\frac{2}{x_{max}-x_{min}}$ at $x=x_{med}$. If $x_{min}=x_{med}=x_{max}$ then $x=x_{med}$ with probability 1; otherwise the triangular distribution has PDF:

$$\begin{array}{c}\begin{array}{cc}f\left(x\right)=\frac{x-x_{min}}{x_{med}-x_{min}}\times \frac{2}{x_{max}-x_{min}}& \text{if}{x}_{min}\le x\le x_{med}\text{,}\\ & \\ & \\ f\left(x\right)=\frac{x_{max}-x}{x_{max}-x_{med}}\times \frac{2}{x_{max}-x_{min}}& \text{if}{x}_{med}<x\le x_{max}\text{,}\\ & \\ & \\ f\left(x\right)=0& \text{otherwise.}\end{array}\end{array}$$

One of the initialization functions init_repeat() (for a repeatable sequence if computed sequentially) or init_nonrepeat() (for a non-repeatable sequence) must be called prior to the first call to dist_triangular.

References

Knuth, D E, 1981, The Art of Computer Programming (Volume 2), (2nd Edition), Addison–Wesley