help for gausshermite                                      Jean-Benoit Hardouin

Estimation of integrals using Gauss Hermite quadratures

gausshermite function , sigma(#) mu(#) nodes(#) display


gausshermite estimate the integrals of the form f(x)g(x/mu,sigma) on all the reals where g(x/mu,sigma) is the gaussian distribution function with mean mu and variance sigma^2.


function define f(x). For example, if f(x)=x^2, function is x^2. It is necessary to use x for the variable of integration.

mu define the mean of x (0 by default).

sigma define the standard deviation of x (1 by default).

nodes define the number of quadrature nodes (12 by default).

display allow to automatically display the estimation.

Note that the quadrature nodes and the associated weights are computed using the ghquadm Stata command. Find this command with findit ghquadm.


. gausshermite x^2

. gausshermite x^4+exp(x)-2, sigma(1.5) mu(-.4) d n(10)


The estimated value of the integral is saved in r(int).


Jean-Benoit Hardouin, Regional Health Observatory (ORS) - 1, rue Porte Madeleine - BP 2439 - 45032 Orleans Cedex 1 - France. You can contact the author at jean-benoit.hardouin@orscentre.org and visit