scipy.stats.vonmises¶

scipy.stats.vonmises = <scipy.stats.distributions.vonmises_gen object at 0x4dd23d0>[source]

A Von Mises continuous random variable.

Continuous random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:

Parameters : x : array_like quantiles q : array_like lower or upper tail probability kappa : array_like shape parameters loc : array_like, optional location parameter (default=0) scale : array_like, optional scale parameter (default=1) size : int or tuple of ints, optional shape of random variates (default computed from input arguments ) moments : str, optional composed of letters [‘mvsk’] specifying which moments to compute where ‘m’ = mean, ‘v’ = variance, ‘s’ = (Fisher’s) skew and ‘k’ = (Fisher’s) kurtosis. (default=’mv’) Alternatively, the object may be called (as a function) to fix the shape, location, and scale parameters returning a “frozen” continuous RV object: rv = vonmises(kappa, loc=0, scale=1) Frozen RV object with the same methods but holding the given shape, location, and scale fixed.

Notes

If x is not in range or loc is not in range it assumes they are angles and converts them to [-pi, pi] equivalents.

The probability density function for vonmises is:

```vonmises.pdf(x, kappa) = exp(kappa * cos(x)) / (2*pi*I[0](kappa))
```

for -pi <= x <= pi, kappa > 0.

Examples

```>>> from scipy.stats import vonmises
>>> numargs = vonmises.numargs
>>> [ kappa ] = [0.9,] * numargs
>>> rv = vonmises(kappa)
```

Display frozen pdf

```>>> x = np.linspace(0, np.minimum(rv.dist.b, 3))
>>> h = plt.plot(x, rv.pdf(x))
```

Here, rv.dist.b is the right endpoint of the support of rv.dist.

Check accuracy of cdf and ppf

```>>> prb = vonmises.cdf(x, kappa)
>>> h = plt.semilogy(np.abs(x - vonmises.ppf(prb, kappa)) + 1e-20)
```

Random number generation

```>>> R = vonmises.rvs(kappa, size=100)
```

Methods

 rvs(kappa, loc=0, scale=1, size=1) 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 density function. logcdf(x, kappa, loc=0, scale=1) Log of the cumulative density function. sf(x, kappa, loc=0, scale=1) Survival function (1-cdf — 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, kappa, loc=0, scale=1) Parameter estimates for generic data. expect(func, 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 alpha percent of the distribution

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