# scipy.stats.vonmises

scipy.stats.vonmises = <scipy.stats._continuous_distns.vonmises_gen object>

  A Von Mises continuous random variable.

  As an instance of the `rv_continuous` class, `vonmises` 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 `vonmises` and `vonmises_line` is:

  \[f(x, \kappa) = \frac{ \exp(\kappa \cos(x)) }{ 2 \pi I_0(\kappa) }\]

  for \(-\pi \le x \le \pi\), \(\kappa > 0\). \(I_0\) is the modified Bessel function of order zero (`scipy.special.i0`).

  `vonmises` is a circular distribution which does not restrict the distribution to a fixed interval. Currently, there is no circular distribution framework in scipy. The `cdf` is implemented such that `cdf(x + 2*np.pi) == cdf(x) + 1`.

  `vonmises_line` is the same distribution, defined on \([-\pi, \pi]\) on the real line. This is a regular (i.e. non-circular) distribution.

  `vonmises` and `vonmises_line` take `kappa` as a shape parameter.

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

  Examples

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

  Calculate the first four moments:

      >>> kappa = 3.99
      >>> mean, var, skew, kurt = vonmises.stats(kappa, moments='mvsk')

  Display the probability density function (`pdf`):

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

  Check accuracy of `cdf` and `ppf`:

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

  Generate random numbers:

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

  And compare the histogram:

      >>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
      >>> ax.legend(loc='best', frameon=False)
      >>> plt.show()

  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(n, kappa, loc=0, scale=1) | Non-central moment of order n
  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(alpha, kappa, loc=0, scale=1) | Endpoints of the range that contains fraction alpha [0, 1] of the distribution

scipy.stats.uniform scipy.stats.vonmises_line