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Fitting a two-parameter inverse Gaussian distribution by maximum likelihood (cl> osed form)

invgausscfvarname[weight] [ifexp] [inrange]

by...:may be used withinvgausscf; see help by.

fweights andaweights are allowed; see help weights.

Description

invgausscffits by maximum likelihood a two-parameter inverse Gaussian distribution to a distribution of a variablevarname. The distribution has probability density function for variable x > 0, location parameter m > 0 and scale parameter l > 0 of (l / 2 pi x^3)^(1/2) exp((-l (x - m)^2 / 2 m^2 x)). For a distribution without covariates the maximum likelihood solution can be obtained directly from closed form solutions.

RemarksThis program is provided in case it is interesting or useful. invgaussfit provides a fuller version, including fitting with covariates and inferential results. Its help file also comments on other commands available that use inverse Gaussian distributions in some way.

Saved results

r(mu)andr(lambda)are the estimated inverse Gaussian parameters.

Examples

. invgausscf mpg

AuthorNicholas J. Cox, Durham University n.j.cox@durham.ac.uk

ReferencesEvans, M., Hastings, N. and Peacock, B. 2000.

Statistical distributions.New York: John Wiley.Johnson, N.L., Kotz, S. and Balakrishnan, N. 1994.

Continuous univariatedistributions: Volume 1.New York: John Wiley.

Also seeOnline: help for pinvgauss (if installed), qinvgauss (if installed) invgaussfit (if installed)