import numpy as np
from pytensor_distributions import triangular as ptd_triangular
from preliz.distributions.distributions import Continuous
from preliz.internal.distribution_helper import all_not_none, pytensor_jit, pytensor_rng_jit
[docs]
class Triangular(Continuous):
r"""
Triangular distribution.
The pdf of this distribution is
.. math::
\begin{cases}
0 & \text{for } x < a, \\
\frac{2(x-a)}{(b-a)(c-a)} & \text{for } a \le x < c, \\[4pt]
\frac{2}{b-a} & \text{for } x = c, \\[4pt]
\frac{2(b-x)}{(b-a)(b-c)} & \text{for } c < x \le b, \\[4pt]
0 & \text{for } b < x.
\end{cases}
.. plot::
:context: close-figs
from preliz import Triangular, style
style.use('preliz-doc')
lowers = [0., -1, 2]
cs = [2., 0., 6.5]
uppers = [4., 1, 8]
for lower, c, upper in zip(lowers, cs, uppers):
scale = upper - lower
c_ = (c - lower) / scale
Triangular(lower, c, upper).plot_pdf()
======== ============================================================================
Support :math:`x \in [lower, upper]`
Mean :math:`\dfrac{lower + upper + c}{3}`
Variance :math:`\dfrac{upper^2 + lower^2 +c^2 - lower*upper - lower*c - upper*c}{18}`
======== ============================================================================
Parameters
----------
lower : float
Lower limit.
c : float
Mode.
upper : float
Upper limit.
"""
def __init__(self, lower=None, c=None, upper=None):
super().__init__()
self.support = (-np.inf, np.inf)
self._parametrization(lower, c, upper)
def _parametrization(self, lower=None, c=None, upper=None):
self.lower = lower
self.c = c
self.upper = upper
self.params = (self.lower, self.c, self.upper)
self.param_names = ("lower", "c", "upper")
self.params_support = ((-np.inf, np.inf), (-np.inf, np.inf), (-np.inf, np.inf))
if all_not_none(lower, c, upper):
self._update(lower, c, upper)
def _update(self, lower, c, upper):
self.lower = np.float64(lower)
self.c = np.float64(c)
self.upper = np.float64(upper)
self.support = (self.lower, self.upper)
self.params = (self.lower, self.c, self.upper)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.lower, self.c, self.upper)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.lower, self.c, self.upper)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.lower, self.c, self.upper)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.lower, self.c, self.upper)
[docs]
def entropy(self):
return ptd_entropy(self.lower, self.c, self.upper)
[docs]
def mean(self):
return ptd_mean(self.lower, self.c, self.upper)
[docs]
def mode(self):
return ptd_mode(self.lower, self.c, self.upper)
[docs]
def var(self):
return ptd_var(self.lower, self.c, self.upper)
[docs]
def std(self):
return ptd_std(self.lower, self.c, self.upper)
[docs]
def skewness(self):
return ptd_skewness(self.lower, self.c, self.upper)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.lower, self.c, self.upper)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.lower, self.c, self.upper)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.lower, self.c, self.upper)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.lower, self.c, self.upper)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.lower, self.c, self.upper)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.lower, self.c, self.upper, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
# Assume symmetry
lower = mean - 6**0.5 * sigma
upper = mean + 6**0.5 * sigma
c = mean
self._update(lower, c, upper)
def _fit_mle(self, sample):
lower = np.min(sample)
upper = np.max(sample)
middle = (np.mean(sample) * 3) - lower - upper
self._update(lower, middle, upper)
@pytensor_jit
def ptd_pdf(x, lower, c, upper):
return ptd_triangular.pdf(x, lower, c, upper)
@pytensor_jit
def ptd_cdf(x, lower, c, upper):
return ptd_triangular.cdf(x, lower, c, upper)
@pytensor_jit
def ptd_ppf(q, lower, c, upper):
return ptd_triangular.ppf(q, lower, c, upper)
@pytensor_jit
def ptd_logpdf(x, lower, c, upper):
return ptd_triangular.logpdf(x, lower, c, upper)
@pytensor_jit
def ptd_entropy(lower, c, upper):
return ptd_triangular.entropy(lower, c, upper)
@pytensor_jit
def ptd_mean(lower, c, upper):
return ptd_triangular.mean(lower, c, upper)
@pytensor_jit
def ptd_mode(lower, c, upper):
return ptd_triangular.mode(lower, c, upper)
@pytensor_jit
def ptd_median(lower, c, upper):
return ptd_triangular.median(lower, c, upper)
@pytensor_jit
def ptd_var(lower, c, upper):
return ptd_triangular.var(lower, c, upper)
@pytensor_jit
def ptd_std(lower, c, upper):
return ptd_triangular.std(lower, c, upper)
@pytensor_jit
def ptd_skewness(lower, c, upper):
return ptd_triangular.skewness(lower, c, upper)
@pytensor_jit
def ptd_kurtosis(lower, c, upper):
return ptd_triangular.kurtosis(lower, c, upper)
@pytensor_jit
def ptd_lmoment1(lower, c, upper):
return ptd_triangular.lmoment1(lower, c, upper)
@pytensor_jit
def ptd_lmoment2(lower, c, upper):
return ptd_triangular.lmoment2(lower, c, upper)
@pytensor_jit
def ptd_lmoment3(lower, c, upper):
return ptd_triangular.lmoment3(lower, c, upper)
@pytensor_jit
def ptd_lmoment4(lower, c, upper):
return ptd_triangular.lmoment4(lower, c, upper)
@pytensor_rng_jit
def ptd_rvs(lower, c, upper, size, rng):
return ptd_triangular.rvs(lower, c, upper, size=size, random_state=rng)
