numpy.random.triangular¶

numpy.random.triangular(left, mode, right, size=None)¶

Draw samples from the triangular distribution.

The triangular distribution is a continuous probability distribution with lower limit left, peak at mode, and upper limit right. Unlike the other distributions, these parameters directly define the shape of the pdf.

Parameters:

Parameters:	left : scalar Lower limit. mode : scalar The value where the peak of the distribution occurs. The value should fulfill the condition `left <= mode <= right`. right : scalar Upper limit, should be larger than left. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.
Returns:	samples : ndarray or scalar The returned samples all lie in the interval [left, right].

left : scalar

Lower limit.

mode : scalar

The value where the peak of the distribution occurs. The value should fulfill the condition left <= mode <= right.

right : scalar

Upper limit, should be larger than left.

size : int or tuple of ints, optional

Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. Default is None, in which case a single value is returned.

Returns:

samples : ndarray or scalar

The returned samples all lie in the interval [left, right].

Notes

The probability density function for the triangular distribution is

$P(x;l, m, r) = \begin{cases} \frac{2(x-l)}{(r-l)(m-l)}& \text{for $l \leq x \leq m$},\\ \frac{2(m-x)}{(r-l)(r-m)}& \text{for $m \leq x \leq r$},\\ 0& \text{otherwise}. \end{cases}$

The triangular distribution is often used in ill-defined problems where the underlying distribution is not known, but some knowledge of the limits and mode exists. Often it is used in simulations.

References

[R269]

Wikipedia, “Triangular distribution” http://en.wikipedia.org/wiki/Triangular_distribution

Examples

Draw values from the distribution and plot the histogram:

>>> import matplotlib.pyplot as plt
>>> h = plt.hist(np.random.triangular(-3, 0, 8, 100000), bins=200,
...              normed=True)
>>> plt.show()

(Source code, png, pdf)

../../_images/numpy-random-triangular-1.png

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