scipy.stats.randint — SciPy v1.15.2 Manual (original) (raw)

scipy.stats.randint = <scipy.stats._discrete_distns.randint_gen object>[source]#

A uniform discrete random variable.

As an instance of the rv_discrete class, randint object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Notes

The probability mass function for randint is:

\[f(k) = \frac{1}{\texttt{high} - \texttt{low}}\]

for \(k \in \{\texttt{low}, \dots, \texttt{high} - 1\}\).

randint takes \(\texttt{low}\) and \(\texttt{high}\) as shape parameters.

The probability mass function above is defined in the “standardized” form. To shift distribution use the loc parameter. Specifically, randint.pmf(k, low, high, loc) is identically equivalent to randint.pmf(k - loc, low, high).

Examples

import numpy as np from scipy.stats import randint import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1)

Calculate the first four moments:

low, high = 7, 31 mean, var, skew, kurt = randint.stats(low, high, moments='mvsk')

Display the probability mass function (pmf):

x = np.arange(low - 5, high + 5) ax.plot(x, randint.pmf(x, low, high), 'bo', ms=8, label='randint pmf') ax.vlines(x, 0, randint.pmf(x, low, high), colors='b', lw=5, alpha=0.5)

Alternatively, the distribution object can be called (as a function) to fix the shape and location. This returns a “frozen” RV object holding the given parameters fixed.

Freeze the distribution and display the frozen pmf:

rv = randint(low, high) ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', ... lw=1, label='frozen pmf') ax.legend(loc='lower center') plt.show()

Check the relationship between the cumulative distribution function (cdf) and its inverse, the percent point function (ppf):

q = np.arange(low, high) p = randint.cdf(q, low, high) np.allclose(q, randint.ppf(p, low, high)) True

Generate random numbers:

r = randint.rvs(low, high, size=1000)

Methods