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.

(Source code, png, hires.png, pdf)



\(x \in \mathbb{R}\)


\(\mu + \nu\)


\(\sigma^2 + \nu^2\)

mutensor_like of float, default 0

Mean of the normal distribution.

sigmatensor_like of float

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

nutensor_like of float

Mean of the exponential distribution (nu > 0).



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


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.


ExGaussian.dist([mu, sigma, nu])

Creates a tensor variable corresponding to the cls distribution.