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# scipy.stats.laplace_asymmetric

scipy.stats.laplace_asymmetric = <scipy.stats._continuous_distns.laplace_asymmetric_gen object>

  An asymmetric Laplace continuous random variable.

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

  Methods

  rvs(kappa, loc=0, scale=1, size=1, random_state=None) | Random variates.
  pdf(x, kappa, loc=0, scale=1) | Probability density function.
  logpdf(x, kappa, loc=0, scale=1) | Log of the probability density function.
  cdf(x, kappa, loc=0, scale=1) | Cumulative distribution function.
  logcdf(x, kappa, loc=0, scale=1) | Log of the cumulative distribution function.
  sf(x, kappa, loc=0, scale=1) | Survival function (also defined as `1 - cdf`, but sf is sometimes more accurate).
  logsf(x, kappa, loc=0, scale=1) | Log of the survival function.
  ppf(q, kappa, loc=0, scale=1) | Percent point function (inverse of `cdf` — percentiles).
  isf(q, kappa, loc=0, scale=1) | Inverse survival function (inverse of `sf`).
  moment(order, kappa, loc=0, scale=1) | Non-central moment of the specified order.
  stats(kappa, loc=0, scale=1, moments=’mv’) | Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
  entropy(kappa, loc=0, scale=1) | (Differential) entropy of the RV.
  fit(data) | Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments.
  expect(func, args=(kappa,), 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(kappa, loc=0, scale=1) | Median of the distribution.
  mean(kappa, loc=0, scale=1) | Mean of the distribution.
  var(kappa, loc=0, scale=1) | Variance of the distribution.
  std(kappa, loc=0, scale=1) | Standard deviation of the distribution.
  interval(confidence, kappa, loc=0, scale=1) | Confidence interval with equal areas around the median.

  See also

  `laplace`

    Laplace distribution

  Notes

  The probability density function for `laplace_asymmetric` is

  \[\begin{split}f(x, \kappa) &= \frac{1}{\kappa+\kappa^{-1}}\exp(-x\kappa),\quad x\ge0\\ &= \frac{1}{\kappa+\kappa^{-1}}\exp(x/\kappa),\quad x<0\\\end{split}\]

  for \(-\infty < x < \infty\), \(\kappa > 0\).

  `laplace_asymmetric` takes `kappa` as a shape parameter for \(\kappa\). For \(\kappa = 1\), it is identical to a Laplace distribution.

  The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the `loc` and `scale` parameters. Specifically, `laplace_asymmetric.pdf(x, kappa, loc, scale)` is identically equivalent to `laplace_asymmetric.pdf(y, kappa) / scale` with `y = (x - loc) / scale`. Note that shifting the location of a distribution does not make it a “noncentral” distribution; noncentral generalizations of some distributions are available in separate classes.

  Note that the scale parameter of some references is the reciprocal of SciPy’s `scale`. For example, \(\lambda = 1/2\) in the parameterization of [1] is equivalent to `scale = 2` with `laplace_asymmetric`.

  References

  [1]

  “Asymmetric Laplace distribution”, Wikipedia https://en.wikipedia.org/wiki/Asymmetric_Laplace_distribution

  [2]

  Kozubowski TJ and Podgórski K. A Multivariate and Asymmetric Generalization of Laplace Distribution, Computational Statistics 15, 531–540 (2000). DOI:10.1007/PL00022717

  Examples

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

  Get the support:

      >>> kappa = 2
      >>> lb, ub = laplace_asymmetric.support(kappa)

  Calculate the first four moments:

      >>> mean, var, skew, kurt = laplace_asymmetric.stats(kappa, moments='mvsk')

  Display the probability density function (`pdf`):

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

  Check accuracy of `cdf` and `ppf`:

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

  Generate random numbers:

      >>> r = laplace_asymmetric.rvs(kappa, size=1000)

  And compare the histogram:

      >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
      >>> ax.set_xlim([x[0], x[-1]])
      >>> ax.legend(loc='best', frameon=False)
      >>> plt.show()