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# 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.

  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

  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.