help for weibullfit

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(bpar) and e(cpar) 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.

Note September 2014

The parameters denoted b and c above are now denoted
bpar and cpar in program output and the saved results
e(bpar) and e(cpar). This is to avoid being bitten as a
side-effect of changes in Stata official code. In essence, a
user-written program of this kind cannot name a parameter b
without a collision in name space. We thank Zarek C. Brot-Goldberg for
alerting us to the problem and Isabel Cañette of StataCorp for
confirmation of its diagnosis. We understand that StataCorp intend to
fix the problem in a future update.

Examples

. weibullfit mpg

Authors

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

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