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# scipy.stats.gennorm

`scipy.stats.``gennorm` = <scipy.stats._continuous_distns.gennorm_gen object>

  A generalized normal continuous random variable.

  As an instance of the `rv_continuous` class, `gennorm` 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.

  See also

  `laplace`
    Laplace distribution
  `norm`
    normal distribution

  Notes

  The probability density function for `gennorm` is [R587]:

                                   beta
      gennorm.pdf(x, beta) =  ---------------  exp(-|x|**beta)
                              2 gamma(1/beta)

  `gennorm` takes `beta` as a shape parameter. For `beta = 1`, it is identical to a Laplace distribution. For `beta = 2`, it is identical to a normal distribution (with `scale=1/sqrt(2)`).

  References

  [R587] | (1, 2) “Generalized normal distribution, Version 1”, https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1

  Examples

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

  Calculate a few first moments:

      >>> beta = 1.3
      >>> mean, var, skew, kurt = gennorm.stats(beta, moments='mvsk')

  Display the probability density function (`pdf`):

      >>> x = np.linspace(gennorm.ppf(0.01, beta),
      ...                 gennorm.ppf(0.99, beta), 100)
      >>> ax.plot(x, gennorm.pdf(x, beta),
      ...        'r-', lw=5, alpha=0.6, label='gennorm 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 = gennorm(beta)
      >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

  Check accuracy of `cdf` and `ppf`:

      >>> vals = gennorm.ppf([0.001, 0.5, 0.999], beta)
      >>> np.allclose([0.001, 0.5, 0.999], gennorm.cdf(vals, beta))
      True

  Generate random numbers:

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