numpy.random.
triangular
Draw samples from the triangular distribution over the interval [left, right].
[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.
Note
New code should use the triangular method of a default_rng() instance instead; see random-quick-start.
default_rng()
Lower limit.
The value where the peak of the distribution occurs. The value must fulfill the condition left <= mode <= right.
left <= mode <= right
Upper limit, must be larger than left.
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.
(m, n, k)
m * n * k
None
left
mode
right
np.broadcast(left, mode, right).size
Drawn samples from the parameterized triangular distribution.
See also
Generator.triangular
which should be used for new code.
Notes
The probability density function for the triangular distribution is
System Message: WARNING/2 (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} )
latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2017-04-15> Babel <3.18> and hyphenation patterns for 3 language(s) loaded. (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty (/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def (/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu) (/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu) (/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu))) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.8 \usepackage {bm}^^M No pages of output. Transcript written on math.log.
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
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 >>> h = plt.hist(np.random.triangular(-3, 0, 8, 100000), bins=200, ... density=True) >>> plt.show()