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# scipy.stats.genexpon

`scipy.stats.``genexpon` = <scipy.stats._continuous_distns.genexpon_gen object at 0x45047fcc>

  A generalized exponential continuous random variable.

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

      genexpon.pdf(x, a, b, c) = (a + b * (1 - exp(-c*x))) *                                    exp(-a*x - b*x + b/c * (1-exp(-c*x)))

  for `x >= 0`, `a, b, c > 0`.

  `genexpon` takes `a`, `b` and `c` 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, `genexpon.pdf(x, a, b, c, loc, scale)` is identically equivalent to `genexpon.pdf(y, a, b, c) / scale` with `y = (x - loc) / scale`.

  References

  H.K. Ryu, “An Extension of Marshall and Olkin’s Bivariate Exponential Distribution”, Journal of the American Statistical Association, 1993.

  > N. Balakrishnan, “The Exponential Distribution: Theory, Methods and Applications”, Asit P. Basu.

  Examples

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

  Calculate a few first moments:

      >>> a, b, c = 9.13, 16.2, 3.28
      >>> mean, var, skew, kurt = genexpon.stats(a, b, c, moments='mvsk')

  Display the probability density function (`pdf`):

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

  Check accuracy of `cdf` and `ppf`:

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

  Generate random numbers:

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