def rvs(self, *args, **kwargs):
'''
Random variates of given type.
:param loc: (*float*) location parameter (default=0).
:param scale: (*float*) scale parameter (default=1).
:param size: (*int*) Size.
:returns: Probability density function.
'''
dist = self._create_distribution(*args)
size = kwargs.pop('size', 1)
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def exponential(scale=1.0, size=None):
"""
Draw samples from a exponential distribution.
:param scale: (*float*) The scale parameter.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized exponential distribution.
"""
dist = ExponentialDistribution(scale)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def weibull(a, size=None):
"""
Draw samples from a Weibull distribution.
:param a: (*float*) Shape parameter of the distribution. Must be nonnegative.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized Weibull distribution.
"""
dist = WeibullDistribution(a, 1)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def chisquare(df, size=None):
"""
Draw samples from a chi-square distribution.
:param df: (*float*) Number of degrees of freedom, should be > 0.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized chisquare distribution.
"""
dist = ChiSquaredDistribution(df)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def pareto(a, size=None):
"""
Draw samples from a Pareto II or Lomax distribution with specified shape.
:param a: (*float*) Shape of the distribution. Should be greater than zero.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized Pareto distribution.
"""
dist = ParetoDistribution(1, a)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def rvs(self, *args, **kwargs):
'''
Random variates of given type.
:param loc: (*float*) location parameter (default=0).
:param scale: (*float*) scale parameter (default=1).
:param size: (*int*) Size.
:returns: Probability density function.
'''
dist = self._create_distribution(*args)
size = kwargs.pop('size', 1)
r = DistributionUtil.rvs(dist, size)
return MIArray(r)
def normal(loc=0.0, scale=1.0, size=None):
"""
Draw random samples from a normal (Gaussian) distribution.
:param loc: (*float*) Mean (“centre”) of the distribution.
:param scale: (*float*) Standard deviation (spread or “width”) of the distribution.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
"""
dist = NormalDistribution(loc, scale)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def standard_t(df, size=None):
"""
Draw samples from a standard Student’s t distribution with df degrees of freedom.
:param df: (*float*) Degrees of freedom, should be > 0.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized Student’s t distribution.
"""
dist = TDistribution(df)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def lognormal(mean=0.0, sigma=1.0, size=None):
"""
Draw samples from the log-normal distribution.
:param mean: (*float*) Mean value of the underlying normal distribution. Default is 0.
:param sigma: (*float*) Standard deviation of the underlying normal distribution. Should be greater than zero. Default is 1.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized log-normal distribution.
"""
dist = LogNormalDistribution(loc, scale)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def logistic(loc=0.0, scale=1.0, size=None):
"""
Draw samples from the Logistic distribution.
:param loc: (*float*) Mean (“centre”) of the distribution.
:param scale: (*float*) Standard deviation (spread or “width”) of the distribution.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized Logistic distribution.
"""
dist = LogisticDistribution(loc, scale)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def laplace(loc=0.0, scale=1.0, size=None):
"""
Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay).
:param loc: (*float*) Mean (“centre”) of the distribution.
:param scale: (*float*) Standard deviation (spread or “width”) of the distribution.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized Laplace distribution.
"""
dist = LaplaceDistribution(loc, scale)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def gamma(shape, scale=1.0, size=None):
"""
Draw random samples from a Gamma distribution.
:param shape: (*float*) The shape of the gamma distribution. Should be greater than zero.
:param scale: (*float*) Standard deviation (spread or “width”) of the distribution.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized Gamma distribution.
"""
dist = GammaDistribution(shape, scale)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def f(dfnum, dfden, size=None):
"""
Draw random samples from a F distribution.
:param dfnum: (*float*) Degrees of freedom in numerator, should be > 0.
:param dfden: (*float*) Degrees of freedom in denominator, should be > 0.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized Fisher distribution.
"""
dist = FDistribution(dfnum, dfden)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def cdf(self, x, *args, **kwargs):
'''
Cumulative distribution function of the given RV.
:param x: (*array_like*) quantiles.
:param loc: (*float*) location parameter (default=0).
:param scale: (*float*) scale parameter (default=1).
:returns: Cumulative distribution function.
'''
dist = self._create_distribution(*args)
if isinstance(x, (list, tuple)):
x = np.array(x)
if isinstance(x, NDArray):
x = x._array
r = DistributionUtil.cdf(dist, x)
return NDArray(r)
def uniform(low=0.0, high=1.0, size=None):
"""
Draw samples from the uniform distribution.
:param low: (*float*) Lower boundary of the output interval. All values generated will
be greater than or equal to low. The default value is 0.
:param high: (*float*) Upper boundary of the output interval. All values generated will
be less than high. The default value is 1.0.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized uniform distribution.
"""
dist = UniformRealDistribution(low, high)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def cdf(self, x, *args, **kwargs):
'''
Cumulative distribution function of the given RV.
:param x: (*array_like*) quantiles.
:param loc: (*float*) location parameter (default=0).
:param scale: (*float*) scale parameter (default=1).
:returns: Cumulative distribution function.
'''
dist = self._create_distribution(*args)
if isinstance(x, (list, tuple)):
x = minum.array(x)
if isinstance(x, MIArray):
x = x.array
r = DistributionUtil.cdf(dist, x)
return MIArray(r)
def logpdf(self, x, *args, **kwargs):
'''
Log of the probability density function at x of the given RV.
:param x: (*array_like*) quantiles.
:param loc: (*float*) location parameter (default=0).
:param scale: (*float*) scale parameter (default=1).
:returns: Log of the probability density function.
'''
dist = self._create_distribution(*args)
if isinstance(x, (list, tuple)):
x = minum.array(x)
if isinstance(x, MIArray):
x = x.array
r = DistributionUtil.logpdf(dist, x)
return MIArray(r)
def ppf(self, x, *args, **kwargs):
'''
Percent point function (inverse of cdf) at q of the given RV.
:param q: (*array_like*) lower tail probability.
:param loc: (*float*) location parameter (default=0).
:param scale: (*float*) scale parameter (default=1).
:returns: Quantile corresponding to the lower tail probability q.
'''
dist = self._create_distribution(*args)
if isinstance(x, (list, tuple)):
x = minum.array(x)
if isinstance(x, MIArray):
x = x.array
r = DistributionUtil.ppf(dist, x)
return MIArray(r)
def triangular(left, mode, right, size=None):
"""
Draw samples from the triangular distribution over the interval [left, right].
:param left: (*float*) Lower limit.
:param mode: (*float*) The value where the peak of the distribution occurs. The value
should fulfill the condition left <= mode <= right.
:param right: (*float*) Upper limit, should be larger than left.
:param size: (*int*) Output shape. If size is None (default), a single value is returned.
:returns: (*ndarray or scalar*) Drawn samples from the parameterized triangular distribution.
"""
dist = TriangularDistribution(left, mode, right)
if size is None:
size = 1
r = DistributionUtil.rvs(dist, size)
return NDArray(r)
def ppf(self, x, *args, **kwargs):
'''
Percent point function (inverse of cdf) at q of the given RV.
:param q: (*array_like*) lower tail probability.
:param loc: (*float*) location parameter (default=0).
:param scale: (*float*) scale parameter (default=1).
:returns: Quantile corresponding to the lower tail probability q.
'''
dist = self._create_distribution(*args)
if isinstance(x, (list, tuple)):
x = np.array(x)
if isinstance(x, NDArray):
x = x._array
r = DistributionUtil.ppf(dist, x)
return NDArray(r)
def pmf(self, x, *args, **kwargs):
'''
Probability mass function (PMF) of the given RV.
:param x: (*array_like*) quantiles.
:param loc: (*float*) location parameter (default=0).
:param scale: (*float*) scale parameter (default=1).
:returns: Probability mas function.
'''
dist = self._create_distribution(*args)
if isinstance(x, (list, tuple)):
x = minum.array(x)
if isinstance(x, NDArray):
x = x.array
r = DistributionUtil.pmf(dist, x)
return NDArray(r)
def logpdf(self, x, *args, **kwargs):
'''
Log of the probability density function at x of the given RV.
:param x: (*array_like*) quantiles.
:param loc: (*float*) location parameter (default=0).
:param scale: (*float*) scale parameter (default=1).
:returns: Log of the probability density function.
'''
dist = self._create_distribution(*args)
if isinstance(x, (list, tuple)):
x = np.array(x)
if isinstance(x, NDArray):
x = x._array
r = DistributionUtil.logpdf(dist, x)
return NDArray(r)
