scipy.stats.hypergeom#
- scipy.stats.hypergeom = <scipy.stats._discrete_distns.hypergeom_gen object>[source]#
- A hypergeometric discrete random variable. - The hypergeometric distribution models drawing objects from a bin. M is the total number of objects, n is total number of Type I objects. The random variate represents the number of Type I objects in N drawn without replacement from the total population. - As an instance of the - rv_discreteclass,- hypergeomobject inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.- See also - Notes - The symbols used to denote the shape parameters (M, n, and N) are not universally accepted. See the Examples for a clarification of the definitions used here. - The probability mass function is defined as, \[p(k, M, n, N) = \frac{\binom{n}{k} \binom{M - n}{N - k}} {\binom{M}{N}}\]- for \(k \in [\max(0, N - M + n), \min(n, N)]\), where the binomial coefficients are defined as, \[\binom{n}{k} \equiv \frac{n!}{k! (n - k)!}.\]- This distribution uses routines from the Boost Math C++ library for the computation of the - pmf,- cdf,- sfand- statsmethods. [1]- The probability mass function above is defined in the “standardized” form. To shift distribution use the - locparameter. Specifically,- hypergeom.pmf(k, M, n, N, loc)is identically equivalent to- hypergeom.pmf(k - loc, M, n, N).- References [1]- The Boost Developers. “Boost C++ Libraries”. https://www.boost.org/. - Examples - >>> import numpy as np >>> from scipy.stats import hypergeom >>> import matplotlib.pyplot as plt - Suppose we have a collection of 20 animals, of which 7 are dogs. Then if we want to know the probability of finding a given number of dogs if we choose at random 12 of the 20 animals, we can initialize a frozen distribution and plot the probability mass function: - >>> [M, n, N] = [20, 7, 12] >>> rv = hypergeom(M, n, N) >>> x = np.arange(0, n+1) >>> pmf_dogs = rv.pmf(x) - >>> fig = plt.figure() >>> ax = fig.add_subplot(111) >>> ax.plot(x, pmf_dogs, 'bo') >>> ax.vlines(x, 0, pmf_dogs, lw=2) >>> ax.set_xlabel('# of dogs in our group of chosen animals') >>> ax.set_ylabel('hypergeom PMF') >>> plt.show()   - Instead of using a frozen distribution we can also use - hypergeommethods directly. To for example obtain the cumulative distribution function, use:- >>> prb = hypergeom.cdf(x, M, n, N) - And to generate random numbers: - >>> R = hypergeom.rvs(M, n, N, size=10) - Methods - rvs(M, n, N, loc=0, size=1, random_state=None) - Random variates. - pmf(k, M, n, N, loc=0) - Probability mass function. - logpmf(k, M, n, N, loc=0) - Log of the probability mass function. - cdf(k, M, n, N, loc=0) - Cumulative distribution function. - logcdf(k, M, n, N, loc=0) - Log of the cumulative distribution function. - sf(k, M, n, N, loc=0) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(k, M, n, N, loc=0) - Log of the survival function. - ppf(q, M, n, N, loc=0) - Percent point function (inverse of - cdf— percentiles).- isf(q, M, n, N, loc=0) - Inverse survival function (inverse of - sf).- stats(M, n, N, loc=0, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(M, n, N, loc=0) - (Differential) entropy of the RV. - expect(func, args=(M, n, N), loc=0, lb=None, ub=None, conditional=False) - Expected value of a function (of one argument) with respect to the distribution. - median(M, n, N, loc=0) - Median of the distribution. - mean(M, n, N, loc=0) - Mean of the distribution. - var(M, n, N, loc=0) - Variance of the distribution. - std(M, n, N, loc=0) - Standard deviation of the distribution. - interval(confidence, M, n, N, loc=0) - Confidence interval with equal areas around the median.