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# scipy.stats.exponnorm

`scipy.stats.``exponnorm` = <scipy.stats._continuous_distns.exponnorm_gen object>

  An exponentially modified Normal continuous random variable.

  As an instance of the `rv_continuous` class, `exponnorm` 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 `exponnorm` is:

      exponnorm.pdf(x, K) =
          1/(2*K) exp(1/(2 * K**2)) exp(-x / K) * erfc-(x - 1/K) / sqrt(2))

  where the shape parameter `K > 0`.

  It can be thought of as the sum of a normally distributed random value with mean `loc` and sigma `scale` and an exponentially distributed random number with a pdf proportional to `exp(-lambda * x)` where `lambda = (K * scale)**(-1)`.

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

  An alternative parameterization of this distribution (for example, in Wikipedia) involves three parameters, \(\mu\), \(\lambda\) and \(\sigma\). In the present parameterization this corresponds to having `loc` and `scale` equal to \(\mu\) and \(\sigma\), respectively, and shape parameter \(K = 1/\sigma\lambda\).

  New in version 0.16.0.

  Examples

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

  Calculate a few first moments:

      >>> K = 1.5
      >>> mean, var, skew, kurt = exponnorm.stats(K, moments='mvsk')

  Display the probability density function (`pdf`):

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

  Check accuracy of `cdf` and `ppf`:

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

  Generate random numbers:

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