`scipy.stats._probability_distribution:_ProbabilityDistribution.logpmf`

source: /scipy/stats/_probability_distribution.py :939

Signature

def logpmf ( self , x , / , method = None )

Summary

Log of the probability mass function

Extended Summary

The probability mass function ("PMF"), denoted $f (x)$ , is the probability that the random variable $X$ will assume the value $x$ .

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

logpmf computes the logarithm of the probability mass function ("log-PMF"), $lo g (f (x))$ , but it may be numerically favorable compared to the naive implementation (computing $f (x)$ and taking the logarithm).

logpmf accepts x for $x$ .

Parameters

x : array_like

The argument of the log-PMF.

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

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

'formula': use a formula for the log-PMF itself
'logexp': evaluate the PMF and takes its logarithm

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 log-PMF evaluated at the argument x.

Notes

Suppose a discrete probability distribution has support over the integers $l, l + 1, ..., r - 1, r$ . By definition of the support, the log-PMF evaluates to its minimum value of $- \infty$ (i.e. $lo g (0)$ ) for non-integral $x$ and for $x$ outside the support; i.e. for $x < l$ or $x > r$ .

For distributions with infinite support, it is common for pmf to return a value of 0 when the argument is theoretically within the support; this can occur because the true value of the PMF is too small to be represented by the chosen dtype. The log-PMF, however, will often be finite (not -inf) over a much larger domain. Consequently, it may be preferred to work with the logarithms of probabilities and probability densities to avoid underflow.

Examples

Instantiate a distribution with the desired parameters:

import numpy as np
from scipy import stats
X = stats.Binomial(n=10, p=0.5)

✓

Evaluate the log-PMF at the desired argument:

X.logpmf(5)

✗

np.allclose(X.logpmf(5), np.log(X.pmf(5)))

✓

Aliases

scipy.stats._distribution_infrastructure._ProbabilityDistribution.logpmf