The use of interior penalty functions to overcome lognormal distribution parameter estimation anomalies

Abstract

The maximum likelihood statistical modelling problems for the three-and four-parameter lognormal distributions possess the unusual future that the theoretical maximum likelihood parameter estimates are inadmissible values for which the likelihood function is postively infinite. Accordingly, “local-maximum” likelihood parameter estimates corresponding to the primary relative maximum of the likelihood function must be derived. Although these estimates often possess many of the properties associated with ordinary maximum likelihood estimates, their numerical computation is not altogether straightforward since solutions corresponding to the global maximum of the likelihood function must be avoided. A procedure for overcoming these estimation anomalies is presented. The numerical examples also presented and discussed indicate that the procedure, which employs interior penalty function techniques, is robust. Extensive practical experience with the procedure supports this conclusion.

^†All correspondence regarding this paper should be addressed to the author at 5480 Cornell Drive, Chicago, Illinois 60637, U.S.A

^†All correspondence regarding this paper should be addressed to the author at 5480 Cornell Drive, Chicago, Illinois 60637, U.S.A

Notes

^†All correspondence regarding this paper should be addressed to the author at 5480 Cornell Drive, Chicago, Illinois 60637, U.S.A