6.3.12.1.5. statsmodels.sandbox.distributions.sppatch.expect_v2

statsmodels.sandbox.distributions.sppatch.expect_v2(self, fn=None, args=(), loc=0, scale=1, lb=None, ub=None, conditional=False)

calculate expected value of a function with respect to the distribution

location and scale only tested on a few examples

Parameters:

all parameters are keyword parameters

fn

: function (default: identity mapping)

Function for which integral is calculated. Takes only one argument.

args

: tuple

argument (parameters) of the distribution

lb, ub

: numbers

lower and upper bound for integration, default is set using quantiles of the distribution, see Notes

conditional

: boolean (False)

If true then the integral is corrected by the conditional probability of the integration interval. The return value is the expectation of the function, conditional on being in the given interval.

Returns:

expected value : float

Notes

This function has not been checked for it’s behavior when the integral is not finite. The integration behavior is inherited from scipy.integrate.quad.

The default limits are lb = self.ppf(1e-9, *args), ub = self.ppf(1-1e-9, *args)

For some heavy tailed distributions, ‘alpha’, ‘cauchy’, ‘halfcauchy’, ‘levy’, ‘levy_l’, and for ‘ncf’, the default limits are not set correctly even when the expectation of the function is finite. In this case, the integration limits, lb and ub, should be chosen by the user. For example, for the ncf distribution, ub=1000 works in the examples.

There are also problems with numerical integration in some other cases, for example if the distribution is very concentrated and the default limits are too large.