scipy.stats.randint

scipy.stats.randint = <scipy.stats._discrete_distns.randint_gen object>

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.

Methods

rvs(low, high, loc=0, size=1, random_state=None)	Random variates.
pmf(k, low, high, loc=0)	Probability mass function.
logpmf(k, low, high, loc=0)	Log of the probability mass function.
cdf(k, low, high, loc=0)	Cumulative distribution function.
logcdf(k, low, high, loc=0)	Log of the cumulative distribution function.
sf(k, low, high, loc=0)	Survival function (also defined as 1 - cdf, but sf is sometimes more accurate).
logsf(k, low, high, loc=0)	Log of the survival function.
ppf(q, low, high, loc=0)	Percent point function (inverse of cdf — percentiles).
isf(q, low, high, loc=0)	Inverse survival function (inverse of sf).
stats(low, high, loc=0, moments=’mv’)	Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(low, high, loc=0)	(Differential) entropy of the RV.
expect(func, args=(low, high), loc=0, lb=None, ub=None, conditional=False)	Expected value of a function (of one argument) with respect to the distribution.
median(low, high, loc=0)	Median of the distribution.
mean(low, high, loc=0)	Mean of the distribution.
var(low, high, loc=0)	Variance of the distribution.
std(low, high, loc=0)	Standard deviation of the distribution.
interval(confidence, low, high, loc=0)	Confidence interval with equal areas around the median.

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

Try it in your browser!

>>> 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)

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