numpy.random.RandomState.triangular

RandomState.triangular(left, mode, right, size=None)

Draw samples from the triangular distribution over the interval [left, right].

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:

left : float or array_like of floats

Lower limit.

mode : float or array_like of floats

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

right : float or array_like of floats

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. If size is None (default), a single value is returned if left, mode, and right are all scalars. Otherwise, np.broadcast(left, mode, right).size samples are drawn.

Returns:

out : ndarray or scalar

Drawn samples from the parameterized triangular distribution.

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(r-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

[1]	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,
...              density=True)
>>> plt.show()