flopscope.numpy.random.Generator.triangular

fnp.random.Generator.triangular(self, left, mode, right, size=None)

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

Adapted from NumPy docs np.random.Generator.triangular

Arearandom

Typecounted

Cost

\text{numel}(\text{output})

Flopscope Context

Triangular distribution; cost = numel(output).

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 must fulfill the condition left <= mode <= right.
right:float or array_like of floats: Upper limit, must 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, flops.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

footnote

1

Wikipedia, "Triangular distribution"
https://en.wikipedia.org/wiki/Triangular_distribution

Examples

Draw values from the distribution and plot the histogram:

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