scipy.stats.hypergeom¶

scipy.stats.hypergeom = <scipy.stats.distributions.hypergeom_gen object at 0x4603890>[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.

Discrete random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:

Parameters : x : array_like quantiles q : array_like lower or upper tail probability M, n, N : array_like shape parameters loc : array_like, optional location parameter (default=0) scale : array_like, optional scale parameter (default=1) size : int or tuple of ints, optional shape of random variates (default computed from input arguments ) moments : str, optional composed of letters [‘mvsk’] specifying which moments to compute where ‘m’ = mean, ‘v’ = variance, ‘s’ = (Fisher’s) skew and ‘k’ = (Fisher’s) kurtosis. (default=’mv’) Alternatively, the object may be called (as a function) to fix the shape and : location parameters returning a “frozen” discrete RV object: : rv = hypergeom(M, n, N, loc=0) : Frozen RV object with the same methods but holding the given shape and location fixed.

Notes

The probability mass function is defined as:

```pmf(k, M, n, N) = choose(n, k) * choose(M - n, N - k) / choose(M, N),
for N - (M-n) <= k <= min(m,N)```

Examples

```>>> from scipy.stats import hypergeom
```

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.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 hypergeom methods 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 variates. pmf(x, M, n, N, loc=0) Probability mass function. logpmf(x, M, n, N, loc=0) Log of the probability mass function. cdf(x, M, n, N, loc=0) Cumulative density function. logcdf(x, M, n, N, loc=0) Log of the cumulative density function. sf(x, M, n, N, loc=0) Survival function (1-cdf — sometimes more accurate). logsf(x, 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, 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(alpha, M, n, N, loc=0) Endpoints of the range that contains alpha percent of the distribution

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