Fitting a two-parameter Weibull distribution by maximum likelihood
weibullfit varname [weight] [if exp] [in range] [, bvar(varlist1) cvar(varlist2) robust cluster(clustervar) level(#) maximize_options ]
by ... : may be used with weibullfit; see help by.
fweights and aweights are allowed; see help weights.
Description
weibullfit fits by maximum likelihood a two-parameter Weibull distribution to a distribution of a variable varname. The distribution has probability density function for variable x >= 0, scale parameter b > 0 and shape parameter c > 0 of (c/b) (x/b)^(c - 1) exp(-(x/b)^c).
Options
bvar(varlist1) and cvar(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.
robust specifies that the Huber/White/sandwich estimator of variance is to be used in place of the traditional calculation. robust combined with cluster() 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. clustervar specifies to which group each observation belongs; e.g., cluster(personid) in data with repeated observations on individuals. Specifying cluster() implies robust.
level(#) specifies the confidence level, in percent, for the confidence intervals of the coefficients; see help level.
nolog suppresses the iteration log.
maximize_options control the maximization process; see help maximize. If you are seeing many "(not concave)" messages in the log, using the difficult option may help convergence.
Saved results
In addition to the usual results saved after ml, weibullfit also saves the following, if no covariates have been specified:
e(b) and e(c) are the estimated Weibull parameters.
The following results are saved regardless of whether covariates have been specified:
e(b_b) and e(b_c) are row vectors containing the parameter estimates from each equation.
e(length_b_b) and e(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
Authors
Nicholas J. Cox, Durham University n.j.cox@durham.ac.uk
Stephen P. Jenkins, University of Essex stephenj@essex.ac.uk
References
Evans, M., Hastings, N. and Peacock, B. 2000. Statistical distributions. New York: John Wiley.
Johnson, N.L., Kotz, S. and Balakrishnan, N. 1994. Continuous univariate distributions: Volume 1. New York: John Wiley.
Kleiber, C. and Kotz, S. 2003. Statistical size distributions in economics and actuarial sciences. Hoboken, NJ: John Wiley.
Also see
Online: help for pweibull (if installed), qweibull (if installed)