scipy.stats.vonmises_line¶
-
scipy.stats.
vonmises_line
= <scipy.stats._continuous_distns.vonmises_gen object>[source]¶ A Von Mises continuous random variable.
As an instance of the
rv_continuous
class,vonmises_line
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
andvonmises_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. Thecdf
is implemented such thatcdf(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
andvonmises_line
takekappa
as a shape parameter.The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the
loc
andscale
parameters. Specifically,vonmises_line.pdf(x, kappa, loc, scale)
is identically equivalent tovonmises_line.pdf(y, kappa) / scale
withy = (x - loc) / scale
.Examples
>>> from scipy.stats import vonmises_line >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> kappa = 3.99 >>> mean, var, skew, kurt = vonmises_line.stats(kappa, moments='mvsk')
Display the probability density function (
pdf
):>>> x = np.linspace(vonmises_line.ppf(0.01, kappa), ... vonmises_line.ppf(0.99, kappa), 100) >>> ax.plot(x, vonmises_line.pdf(x, kappa), ... 'r-', lw=5, alpha=0.6, label='vonmises_line 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_line(kappa) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of
cdf
andppf
:>>> vals = vonmises_line.ppf([0.001, 0.5, 0.999], kappa) >>> np.allclose([0.001, 0.5, 0.999], vonmises_line.cdf(vals, kappa)) True
Generate random numbers:
>>> r = vonmises_line.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, kappa, loc=0, scale=1)
Parameter estimates for generic data.
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 alpha percent of the distribution