Corrected Maximum Likelihood in Non-Regular Problems
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1987 · Volume 49 · Issue 1
DOI: 10.1111/j.2517-6161.1987.tb01430.x
Abstract
Maximum likelihood (ML) estimation can break down for distributions like the three-parameter Weibull or gamma where one of the parameters is a limit of the range of the distribution. It is suggested that use of the product of densities for the likelihood function is a misapplication of theMLmethod in such non-regular cases, and that this is the reason for its failure. It is shown thatMLworks quite satisfactorily if the likelihood is corrected in an appropriate way.
Keywords
maximum likelihood, non-regular estimation, weibull distribution, gamma distribution, spacings
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