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# scipy.stats.gausshyper

`scipy.stats.``gausshyper` = <scipy.stats._continuous_distns.gausshyper_gen object>

  A Gauss hypergeometric continuous random variable.

  As an instance of the `rv_continuous` class, `gausshyper` 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 density function for `gausshyper` is:

      gausshyper.pdf(x, a, b, c, z) =
          C * x**(a-1) * (1-x)**(b-1) * (1+z*x)**(-c)

  for `0 <= x <= 1`, `a > 0`, `b > 0`, and `C = 1 / (B(a, b) F[2, 1](c, a; a+b; -z))`

  `gausshyper` takes `a`, `b`, `c` and `z` as shape parameters.

  The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the `loc` and `scale` parameters. Specifically, `gausshyper.pdf(x, a, b, c, z, loc, scale)` is identically equivalent to `gausshyper.pdf(y, a, b, c, z) / scale` with `y = (x - loc) / scale`.

  Examples

      >>> from scipy.stats import gausshyper
      >>> import matplotlib.pyplot as plt
      >>> fig, ax = plt.subplots(1, 1)

  Calculate a few first moments:

      >>> a, b, c, z = 13.8, 3.12, 2.51, 5.18
      >>> mean, var, skew, kurt = gausshyper.stats(a, b, c, z, moments='mvsk')

  Display the probability density function (`pdf`):

      >>> x = np.linspace(gausshyper.ppf(0.01, a, b, c, z),
      ...                 gausshyper.ppf(0.99, a, b, c, z), 100)
      >>> ax.plot(x, gausshyper.pdf(x, a, b, c, z),
      ...        'r-', lw=5, alpha=0.6, label='gausshyper pdf')

  Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a “frozen” RV object holding the given parameters fixed.

  Freeze the distribution and display the frozen `pdf`:

      >>> rv = gausshyper(a, b, c, z)
      >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

  Check accuracy of `cdf` and `ppf`:

      >>> vals = gausshyper.ppf([0.001, 0.5, 0.999], a, b, c, z)
      >>> np.allclose([0.001, 0.5, 0.999], gausshyper.cdf(vals, a, b, c, z))
      True

  Generate random numbers:

      >>> r = gausshyper.rvs(a, b, c, z, size=1000)

  And compare the histogram:

      >>> ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
      >>> ax.legend(loc='best', frameon=False)
      >>> plt.show()

  (Source code)

  Methods

  `rvs(a, b, c, z, loc=0, scale=1, size=1, random_state=None)` | Random variates.
  `pdf(x, a, b, c, z, loc=0, scale=1)` | Probability density function.
  `logpdf(x, a, b, c, z, loc=0, scale=1)` | Log of the probability density function.
  `cdf(x, a, b, c, z, loc=0, scale=1)` | Cumulative distribution function.
  `logcdf(x, a, b, c, z, loc=0, scale=1)` | Log of the cumulative distribution function.
  `sf(x, a, b, c, z, loc=0, scale=1)` | Survival function (also defined as `1 - cdf`, but sf is sometimes more accurate).
  `logsf(x, a, b, c, z, loc=0, scale=1)` | Log of the survival function.
  `ppf(q, a, b, c, z, loc=0, scale=1)` | Percent point function (inverse of `cdf` — percentiles).
  `isf(q, a, b, c, z, loc=0, scale=1)` | Inverse survival function (inverse of `sf`).
  `moment(n, a, b, c, z, loc=0, scale=1)` | Non-central moment of order n
  `stats(a, b, c, z, loc=0, scale=1, moments='mv')` | Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
  `entropy(a, b, c, z, loc=0, scale=1)` | (Differential) entropy of the RV.
  `fit(data, a, b, c, z, loc=0, scale=1)` | Parameter estimates for generic data.
  `expect(func, args=(a, b, c, z), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)` | Expected value of a function (of one argument) with respect to the distribution.
  `median(a, b, c, z, loc=0, scale=1)` | Median of the distribution.
  `mean(a, b, c, z, loc=0, scale=1)` | Mean of the distribution.
  `var(a, b, c, z, loc=0, scale=1)` | Variance of the distribution.
  `std(a, b, c, z, loc=0, scale=1)` | Standard deviation of the distribution.
  `interval(alpha, a, b, c, z, loc=0, scale=1)` | Endpoints of the range that contains alpha percent of the distribution