Approximate MLEs of the parameters of location-scale models under type II censoring

Abstract

Log-location-scale distributions are widely used parametric models that have fundamental importance in both parametric and semiparametric frameworks. The likelihood equations based on a Type II censored sample from location-scale distributions do not provide explicit solutions for the para-meters. Statistical software is widely available and is based on iterative methods (such as, Newton Raphson Algorithm, EM algorithm etc.), which require starting values near the global maximum. There are also many situations that the specialized software does not handle. This paper provides a method for determining explicit estimators for the location and scale parameters by approximating the likelihood function, where the method does not require any starting values. The performance of the proposed approximate method for the Weibull distribution and Log-Logistic distributions is compared with those based on iterative methods through the use of simulation studies for a wide range of sample size and Type II censoring schemes. Here we also examine the probability coverages of the pivotal quantities based on asymptotic normality. In addition, two examples are given.

Keywords:

• Log-location scale distributions
• Type II censoring
• MLE
• Monte Carlo simulation
• Pivotal quantity

Acknowledgements

The authors wish to thank Ms Sara Quirk for her meticulous proof reading. Of course, all remaining errors are the authors’ own responsibility. AH is supported through a studentship by the Ontario Student Opportunity Trust Fund-Hospital for Sick Children Foundation Student Scholarship Program and ARW is funded through the Discovery Grant Program of the Natural Sciences and Engineering Research Council of Canada (Grant number 44868-03); however the opinions expressed are those of the authors and should not be attributed to any funding agency.