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bundles / scipy latest / scipy / stats / _new_distributions / Uniform

ABCMeta

scipy.stats._new_distributions:Uniform

source: /scipy/stats/_new_distributions.py :342

Signature

def   Uniform ( * ,  a = None ,  b = None ,  ** kwargs )

Members

Summary

Uniform distribution.

Extended Summary

The probability density function of the uniform distribution is:

for . This class accepts one parameterization: a for , b for .

Parameters

tol : positive float, optional

The desired relative tolerance of calculations. Left unspecified, calculations may be faster; when provided, calculations may be more likely to meet the desired accuracy.

validation_policy : {None, "skip_all"}

Specifies the level of input validation to perform. Left unspecified, input validation is performed to ensure appropriate behavior in edge case (e.g. parameters out of domain, argument outside of distribution support, etc.) and improve consistency of output dtype, shape, etc. Pass 'skip_all' to avoid the computational overhead of these checks when rough edges are acceptable.

cache_policy : {None, "no_cache"}

Specifies the extent to which intermediate results are cached. Left unspecified, intermediate results of some calculations (e.g. distribution support, moments, etc.) are cached to improve performance of future calculations. Pass 'no_cache' to reduce memory reserved by the class instance.

Attributes

All parameters are available as attributes.

Methods

support
plot
sample
moment
mean
median
mode
variance
standard_deviation
skewness
kurtosis
pdf
logpdf
cdf
icdf
ccdf
iccdf
logcdf
ilogcdf
logccdf
ilogccdf
entropy
logentropy

Notes

The following abbreviations are used throughout the documentation.

  • PDF: probability density function

  • CDF: cumulative distribution function

  • CCDF: complementary CDF

  • entropy: differential entropy

  • log-F: logarithm of F (e.g. log-CDF)

  • inverse F: inverse function of F (e.g. inverse CDF)

The API documentation is written to describe the API, not to serve as a statistical reference. Effort is made to be correct at the level required to use the functionality, not to be mathematically rigorous. For example, continuity and differentiability may be implicitly assumed. For precise mathematical definitions, consult your preferred mathematical text.

Examples

To use the distribution class, it must be instantiated using keyword parameters corresponding with one of the accepted parameterizations. 
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
from scipy.stats import Uniform
X = Uniform(a=0.09, b=188.73)
✓
For convenience, the ``plot`` method can be used to visualize the density and other functions of the distribution. 
X.plot()
✗
plt.show()
✓
fig-507d612d9edcad14.png
The support of the underlying distribution is available using the ``support`` method. 
X.support()
✓
The numerical values of parameters associated with all parameterizations are available as attributes. 
X.a, X.b, X.ab
✓
To evaluate the probability density/mass function of the underlying distribution at argument ``x=60.45``: 
x = 60.45
X.pdf(x), X.pmf(x)
✓
The cumulative distribution function, its complement, and the logarithm of these functions are evaluated similarly. 
np.allclose(np.exp(X.logccdf(x)), 1 - X.cdf(x))
✓
The inverse of these functions with respect to the argument ``x`` is also available. 
logp = np.log(1 - X.ccdf(x))
np.allclose(X.ilogcdf(logp), x)
✓
Note that distribution functions and their logarithms also have two-argument versions for working with the probability mass between two arguments. The result tends to be more accurate than the naive implementation because it avoids subtractive cancellation. 
y = 120.82
np.allclose(X.ccdf(x, y), 1 - (X.cdf(y) - X.cdf(x)))
✓
There are methods for computing measures of central tendency, dispersion, higher moments, and entropy. 
X.mean(), X.median(), X.mode()
✓
X.variance(), X.standard_deviation()
✓
X.skewness(), X.kurtosis()
✓
np.allclose(X.moment(order=6, kind='standardized'),
            X.moment(order=6, kind='central') / X.variance()**3)
✓
np.allclose(np.exp(X.logentropy()), X.entropy())
✓
Pseudo-random samples can be drawn from the underlying distribution using ``sample``. 
X.sample(shape=(4,))
✗

See also

rv_infrastructure

Tutorial

Aliases

  • scipy.stats.Uniform

Referenced by

This package