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)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifleft
,mode
, andright
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(xl)}{(rl)(ml)}& \text{for $l \leq x \leq m$},\\ \frac{2(rx)}{(rl)(rm)}& \text{for $m \leq x \leq r$},\\ 0& \text{otherwise}. \end{cases}
The triangular distribution is often used in illdefined problems where the underlying distribution is not known, but some knowledge of the limits and mode exists. Often it is used in simulations.
References
[R198] 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)