`scipy.stats._probability_distribution:_ProbabilityDistribution.pdf`

source: build-install/usr/lib/python3.14/site-packages/scipy/stats/_probability_distribution.py:831

Signature

def pdf(self, x, /, method)

Summary

Probability density function

Extended Summary

The probability density function ("PDF"), denoted $f (x)$ , is the probability per unit length that the random variable will assume the value $x$ . Mathematically, it can be defined as the derivative of the cumulative distribution function $F (x)$ :

f (x) = \frac{d}{d x} F (x)

pdf accepts x for $x$ .

Parameters

x : array_like

The argument of the PDF.

method : {None, 'formula', 'logexp'}

The strategy used to evaluate the PDF. By default (None), the infrastructure chooses between the following options, listed in order of precedence.

'formula': use a formula for the PDF itself
'logexp': evaluate the log-PDF and exponentiate

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 PDF evaluated at the argument x.

Notes

Suppose a continuous probability distribution has support $[l, r]$ . By definition of the support, the PDF evaluates to its minimum value of $0$ outside the support; i.e. for $x < l$ or $x > r$ . The maximum of the PDF may be less than or greater than $1$ ; since the value is a probability density, only its integral over the support must equal $1$ .

For discrete distributions, pdf returns inf at supported points and 0 elsewhere.

Examples

Instantiate a distribution with the desired parameters:

from scipy import stats
X = stats.Uniform(a=-1., b=1.)

✓

Evaluate the PDF at the desired argument:

X.pdf(0.25)

✗

np.float64(0.5)

Aliases

scipy.stats._distribution_infrastructure._ProbabilityDistribution.pdf