# mars.tensor.random.triangular¶

mars.tensor.random.triangular(left, mode, right, size=None, chunk_size=None, gpu=None, dtype=None)[source]

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, mt.broadcast(left, mode, right).size samples are drawn.

• chunk_size (int or tuple of int or tuple of ints, optional) – Desired chunk size on each dimension

• gpu (bool, optional) – Allocate the tensor on GPU if True, False as default

• dtype (data-type, optional) – Data-type of the returned tensor.

Returns

out – Drawn samples from the parameterized triangular distribution.

Return type

Tensor or scalar

Notes

The probability density function for the triangular distribution is

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

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
>>> import mars.tensor as mt
>>> h = plt.hist(mt.random.triangular(-3, 0, 8, 100000).execute(), bins=200,
...              normed=True)
>>> plt.show()