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# scipy.stats.halfgennorm

`scipy.stats.``halfgennorm` = <scipy.stats._continuous_distns.halfgennorm_gen object>

  The upper half of a generalized normal continuous random variable.

  As an instance of the `rv_continuous` class, `halfgennorm` 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

  `gennorm`
    generalized normal distribution
  `expon`
    exponential distribution
  `halfnorm`
    half normal distribution

  Notes

  The probability density function for `halfgennorm` is:

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

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

  References

  [R403] | “Generalized normal distribution, Version 1”, https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1

  Examples

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

  Calculate a few first moments:

      >>> beta = 0.675
      >>> mean, var, skew, kurt = halfgennorm.stats(beta, moments='mvsk')

  Display the probability density function (`pdf`):

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

  Check accuracy of `cdf` and `ppf`:

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

  Generate random numbers:

      >>> r = halfgennorm.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 density function.
  `logcdf(x, beta, loc=0, scale=1)` | Log of the cumulative density 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