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Fitting a two-parameter Weibull distribution by maximum likelihood

weibullfitvarname[weight] [ifexp] [inrange] [,bvar(varlist1)cvar(varlist2)robustcluster(clustervar)level(#)maximize_options]

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

fweights andaweights are allowed; see help weights.

Description

weibullfitfits by maximum likelihood a two-parameter Weibull distribution to a distribution of a variablevarname. The distribution has probability density function for variablex>= 0, scale parameterb> 0 and shape parameterc> 0 of (c/b) (x/b)^(c- 1) exp(-(x/b)^c).

Options

bvar(varlist1)andcvar(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.

robustspecifies that the Huber/White/sandwich estimator of variance is to be used in place of the traditional calculation.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. 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,weibullfitalso saves the following, if no covariates have been specified:

e(b)ande(c)are the estimated Weibull parameters.The following results are saved regardless of whether covariates have been specified:

e(b_b)ande(b_c)are row vectors containing the parameter estimates from each equation.

e(length_b_b)ande(length_b_c)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

. weibullfit mpg

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

Stephen P. Jenkins, University of Essex stephenj@essex.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.Kleiber, C. and Kotz, S. 2003.

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

Also seeOnline: help for pweibull (if installed), qweibull (if installed)