scipy.stats.Normal.

pmf#

Normal.pmf(x, /, *, method=None)[source]#

Probability mass function

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

f (x) = P (X = x)

$f(x) = P(X = x)$

pmf accepts x for $x$ .

Parameters:

xarray_like

The argument of the PMF.

method{None, ‘formula’, ‘logexp’}

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

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

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

Returns:

outarray: The PMF evaluated at the argument x.

See also

cdf
logpmf

Notes

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

For continuous distributions, pmf returns 0 at all real arguments.

References

[1]

Probability mass function, Wikipedia, https://en.wikipedia.org/wiki/Probability_mass_function

Examples

Instantiate a distribution with the desired parameters:

>>> from scipy import stats
>>> X = stats.Binomial(n=10, p=0.5)

Evaluate the PMF at the desired argument:

>>> X.pmf(5)
np.float64(0.24609375)