# pymc.ExGaussian#

class pymc.ExGaussian(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, **kwargs)[source]#

Exponentially modified Gaussian log-likelihood.

Results from the convolution of a normal distribution with an exponential distribution.

The pdf of this distribution is

$f(x \mid \mu, \sigma, \tau) = \frac{1}{\nu}\; \exp\left\{\frac{\mu-x}{\nu}+\frac{\sigma^2}{2\nu^2}\right\} \Phi\left(\frac{x-\mu}{\sigma}-\frac{\sigma}{\nu}\right)$

where $$\Phi$$ is the cumulative distribution function of the standard normal distribution.

 Support $$x \in \mathbb{R}$$ Mean $$\mu + \nu$$ Variance $$\sigma^2 + \nu^2$$
Parameters
mutensor_like of float, default 0

Mean of the normal distribution.

sigma

Standard deviation of the normal distribution (sigma > 0).

nu

Mean of the exponential distribution (nu > 0).

References

Rigby2005

Rigby R.A. and Stasinopoulos D.M. (2005). “Generalized additive models for location, scale and shape” Applied Statististics., 54, part 3, pp 507-554.

Lacouture2008

Lacouture, Y. and Couseanou, D. (2008). “How to use MATLAB to fit the ex-Gaussian and other probability functions to a distribution of response times”. Tutorials in Quantitative Methods for Psychology, Vol. 4, No. 1, pp 35-45.

Methods

 ExGaussian.__init__(*args, **kwargs) ExGaussian.dist([mu, sigma, nu]) Creates a tensor variable corresponding to the cls distribution. ExGaussian.logcdf(mu, sigma, nu) Compute the log of the cumulative distribution function for ExGaussian distribution at the specified value. ExGaussian.logp(mu, sigma, nu) Calculate log-probability of ExGaussian distribution at specified value. ExGaussian.moment(size, mu, sigma, nu)

Attributes

 rv_class rv_op