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Fitting a two-parameter gamma distribution by maximum likelihood

gammafitvarname[weight] [ifexp] [inrange] [,alphavar(varlist1)betavar(varlist2)alternativerobustcluster(clustervar)level(#)maximize_options]

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

fweights andaweights are allowed; see help weights.

Description

gammafitfits by maximum likelihood a two-parameter gamma distribution to a distribution of a variablevarname. The distribution has probability density function for variablex>= 0, shape parametera> 0 and scale parameterb> 0 of [1 / (b^agamma(a))]x^(a- 1) exp(-x/b). See also thealternativeoption.

Options

alphavar(varlist1)andbetavar(varlist2)allow the user to specify each parameter as a function of the covariates specified in the respective variable list. A constant term is always included in each equation.

alternativespecifies use of an alternative parameterisation [(b^a/ gamma(a))]x^(a- 1) exp(-bx).

robustspecifies that the Huber/White/sandwich estimator of variance is to be used in place of the traditional calculation; see[U] 23.14Obtaining robust variance estimates.robustcombined withcluster()allows observations which are not independent within cluster (although they must be independent between clusters).

cluster(clustervar)specifies that the observations are independent across groups (clusters) but not necessarily within groups.clustervarspecifies to which group each observation belongs; e.g.,cluster(personid)in data with repeated observations on individuals. See[U] 23.14 Obtaining robust variance estimates. Specifyingcluster()impliesrobust.

level(#)specifies the confidence level, in percent, for the confidence intervals of the coefficients; see help level.

nologsuppresses the iteration log.

maximize_optionscontrol the maximization process; see help maximize. If you are seeing many "(not concave)" messages in the log, using thedifficultoption may help convergence.

Saved resultsIn addition to the usual results saved after

ml,gammafitalso saves the following, if no covariates have been specified:

e(alpha)ande(beta)are the estimated gamma parameters.The following results are saved regardless of whether covariates have been specified:

e(b_alpha)ande(b_beta)are row vectors containing the parameter estimates from each equation.

e(length_b_alpha)ande(length_b_beta)contain the lengths of these vectors. If no covariates are specified in an equation, the corresponding vector has length equal to 1 (the constant term); otherwise, the length is one plus the number of covariates.

Examples

. gammafit mpg

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

Stephen P. Jenkins, London School of Economics s.jenkins@lse.ac.uk

ReferencesForbes, C., Evans, M., Hastings, N. and Peacock, B. 2011.

Statisticaldistributions.Hoboken, NJ: John Wiley.Johnson, N.L., Kotz, S. and Balakrishnan, N. 1994.

Continuous univariatedistributions: Volume 1.New York: John Wiley.Kleiber, C. and Kotz, S. 2003.

Statistical size distributions ineconomics and actuarial sciences.Hoboken, NJ: John Wiley.

Also seeOnline: help for pgamma (if installed), qgamma (if installed)