scipy.stats.randint#
- scipy.stats.randint = <scipy.stats._discrete_distns.randint_gen object>[source]#
- A uniform discrete random variable. - As an instance of the - rv_discreteclass,- randintobject 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 - randintis:\[f(k) = \frac{1}{\texttt{high} - \texttt{low}}\]- for \(k \in \{\texttt{low}, \dots, \texttt{high} - 1\}\). - randinttakes \(\texttt{low}\) and \(\texttt{high}\) as shape parameters.- The probability mass function above is defined in the “standardized” form. To shift distribution use the - locparameter. 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)