scipy.stats.rv_continuous

class scipy.stats.rv_continuous(momtype=1, a=None, b=None, xa=None, xb=None, xtol=1e-14, badvalue=None, name=None, longname=None, shapes=None, extradoc=None)

A generic continuous random variable class meant for subclassing.

rv_continuous is a base class to construct specific distribution classes and instances from for continuous random variables. It cannot be used directly as a distribution.

Parameters :

momtype : int, optional

The type of generic moment calculation to use: 0 for pdf, 1 (default) for ppf.

a : float, optional

Lower bound of the support of the distribution, default is minus infinity.

b : float, optional

Upper bound of the support of the distribution, default is plus infinity.

xa : float, optional

DEPRECATED

xb : float, optional

DEPRECATED

xtol : float, optional

The tolerance for fixed point calculation for generic ppf.

badvalue : object, optional

The value in a result arrays that indicates a value that for which some argument restriction is violated, default is np.nan.

name : str, optional

The name of the instance. This string is used to construct the default example for distributions.

longname : str, optional

This string is used as part of the first line of the docstring returned when a subclass has no docstring of its own. Note: longname exists for backwards compatibility, do not use for new subclasses.

shapes : str, optional

The shape of the distribution. For example "m, n" for a distribution that takes two integers as the two shape arguments for all its methods.

extradoc : str, optional, deprecated

This string is used as the last part of the docstring returned when a subclass has no docstring of its own. Note: extradoc exists for backwards compatibility, do not use for new subclasses.

Notes

Methods that can be overwritten by subclasses

_rvs
_pdf
_cdf
_sf
_ppf
_isf
_stats
_munp
_entropy
_argcheck

There are additional (internal and private) generic methods that can be useful for cross-checking and for debugging, but might work in all cases when directly called.

Frozen Distribution

Alternatively, the object may be called (as a function) to fix the shape, location, and scale parameters returning a “frozen” continuous RV object:

rv = generic(<shape(s)>, loc=0, scale=1)

frozen RV object with the same methods but holding the given shape, location, and scale fixed

Subclassing

New random variables can be defined by subclassing rv_continuous class and re-defining at least the _pdf or the _cdf method (normalized to location 0 and scale 1) which will be given clean arguments (in between a and b) and passing the argument check method.

If positive argument checking is not correct for your RV then you will also need to re-define the _argcheck method.

Correct, but potentially slow defaults exist for the remaining methods but for speed and/or accuracy you can over-ride:

_logpdf, _cdf, _logcdf, _ppf, _rvs, _isf, _sf, _logsf

Rarely would you override _isf, _sf or _logsf, but you could.

Statistics are computed using numerical integration by default. For speed you can redefine this using _stats:

• take shape parameters and return mu, mu2, g1, g2
• If you can’t compute one of these, return it as None
• Can also be defined with a keyword argument moments=<str>, where <str> is a string composed of ‘m’, ‘v’, ‘s’, and/or ‘k’. Only the components appearing in string should be computed and returned in the order ‘m’, ‘v’, ‘s’, or ‘k’ with missing values returned as None.

Alternatively, you can override _munp, which takes n and shape parameters and returns the nth non-central moment of the distribution.

Examples

To create a new Gaussian distribution, we would do the following:

class gaussian_gen(rv_continuous):
    "Gaussian distribution"
    def _pdf:
        ...
    ...

Methods

rvs(<shape(s)>, loc=0, scale=1, size=1)	random variates
pdf(x, <shape(s)>, loc=0, scale=1)	probability density function
logpdf(x, <shape(s)>, loc=0, scale=1)	log of the probability density function
cdf(x, <shape(s)>, loc=0, scale=1)	cumulative density function
logcdf(x, <shape(s)>, loc=0, scale=1)	log of the cumulative density function
sf(x, <shape(s)>, loc=0, scale=1)	survival function (1-cdf — sometimes more accurate)
logsf(x, <shape(s)>, loc=0, scale=1)	log of the survival function
ppf(q, <shape(s)>, loc=0, scale=1)	percent point function (inverse of cdf — quantiles)
isf(q, <shape(s)>, loc=0, scale=1)	inverse survival function (inverse of sf)
moment(n, <shape(s)>, loc=0, scale=1)	non-central n-th moment of the distribution. May not work for array arguments.
stats(<shape(s)>, loc=0, scale=1, moments=’mv’)	mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’)
entropy(<shape(s)>, loc=0, scale=1)	(differential) entropy of the RV.
fit(data, <shape(s)>, loc=0, scale=1)	Parameter estimates for generic data
expect(func=None, args=(), loc=0, scale=1, lb=None, ub=None,	conditional=False, **kwds) Expected value of a function with respect to the distribution. Additional kwd arguments passed to integrate.quad
median(<shape(s)>, loc=0, scale=1)	Median of the distribution.
mean(<shape(s)>, loc=0, scale=1)	Mean of the distribution.
std(<shape(s)>, loc=0, scale=1)	Standard deviation of the distribution.
var(<shape(s)>, loc=0, scale=1)	Variance of the distribution.
interval(alpha, <shape(s)>, loc=0, scale=1)	Interval that with alpha percent probability contains a random realization of this distribution.
__call__(<shape(s)>, loc=0, scale=1)	Calling a distribution instance creates a frozen RV object with the same methods but holding the given shape, location, and scale fixed. See Notes section.
Parameters for Methods
x	(array_like) quantiles
q	(array_like) lower or upper tail probability
<shape(s)>	(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	(string, 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’)
n	(int) order of moment to calculate in method moments