- class scipy.stats.rv_continuous(momtype=1, a=None, b=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.
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.
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.
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.
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
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.
To create a new Gaussian distribution, we would do the following:
class gaussian_gen(rv_continuous): "Gaussian distribution" def _pdf: ... ...
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