`scipy.stats._probability_distribution:_ProbabilityDistribution.cdf`

source: /scipy/stats/_probability_distribution.py :1021

Signature

def cdf ( self , x , y , / , method )

Summary

Cumulative distribution function

Extended Summary

The cumulative distribution function ("CDF"), denoted $F (x)$ , is the probability the random variable $X$ will assume a value less than or equal to $x$ :

F (x) = P (X \leq x)

A two-argument variant of this function is also defined as the probability the random variable $X$ will assume a value between $x$ and $y$ .

F (x, y) = P (x \leq X \leq y)

cdf accepts x for $x$ and y for $y$ .

Parameters

x, y : array_like

The arguments of the CDF. x is required; y is optional.

method : {None, 'formula', 'logexp', 'complement', 'quadrature', 'subtraction'}

The strategy used to evaluate the CDF. By default (None), the one-argument form of the function chooses between the following options, listed in order of precedence.

'formula': use a formula for the CDF itself
'logexp': evaluate the log-CDF and exponentiate
'complement': evaluate the CCDF and take the complement
'quadrature': numerically integrate the PDF (or, in the discrete case, sum the PMF)

In place of 'complement', the two-argument form accepts:

'subtraction': compute the CDF at each argument and take the difference.

Not all method options are available for all distributions. If the selected method is not available, a NotImplementedError will be raised.

Returns

out : array: The CDF evaluated at the provided argument(s).

Notes

Suppose a continuous probability distribution has support $[l, r]$ . The CDF $F (x)$ is related to the probability density function $f (x)$ by:

F (x) = \int_{l}^{x} f (u) d u

The two argument version is:

F (x, y) = \int_{x}^{y} f (u) d u = F (y) - F (x)

The CDF evaluates to its minimum value of $0$ for $x \leq l$ and its maximum value of $1$ for $x \geq r$ .

Suppose a discrete probability distribution has support $[l, r]$ . The CDF $F (x)$ is related to the probability mass function $f (x)$ by:

F (x) = u = l \sum ⌊ x ⌋ f (u)

The CDF evaluates to its minimum value of $0$ for $x < l$ and its maximum value of $1$ for $x \geq r$ .

The CDF is also known simply as the "distribution function".

Examples

Instantiate a distribution with the desired parameters:

from scipy import stats
X = stats.Uniform(a=-0.5, b=0.5)

✓

Evaluate the CDF at the desired argument:

X.cdf(0.25)

✗

Evaluate the cumulative probability between two arguments:

X.cdf(-0.25, 0.25) == X.cdf(0.25) - X.cdf(-0.25)

✗

Aliases

scipy.stats._distribution_infrastructure._ProbabilityDistribution.cdf