The use of L-moments in the analysis of censored data.

Hosking, J. R. M. (1995). The use of L-moments in the analysis of censored data. In: Recent advances in life-testing and reliability, ed. N. Balakrishnan, pp. 545-564. Boca Raton, Fla.: CRC Press.

Abstract. L-moments are summary statistics for probability distributions. They are measures of distributional shape--mean, dispersion, coefficient of variation, skewness, kurtosis, etc.--that are in many ways preferable to the conventional moments. Their statistical applications to complete data samples are described in Hosking (1990). Here we discuss the application of L-moments to the analysis of censored data.

Author's note. Well, that wasn't a very helpful abstract, was it? Perhaps I should try to give a bit more detail. For censored samples, two variants of L-moments can be defined. For example, suppose that values above some threshold are censored, and that only m of the n sample values are actually observed. "A-type" L-moments are just the usual L-moments of the m observed values. "B-type" L-moments are obtained by replacing the n-m censored values by the censoring threshold and computing the L-moments of this "completed sample". The paper shows that several complete-sample techniques based on L-moments can be used with censored samples too. In particular, the L-moment ratio diagram is a useful graphical tool that is easily adapted for use with censored data -- "A-type" L-moments are best for this application. It can give a visual indication of which distributions are candidates for giving a good fit to a given data set. L-moments can also be used to estimate parameters of distributions fitted to a censored data set -- "B-type"L-moments seem best here. For estimation of the Gumbel and generalized extreme value distributions from censored data, L-moments can be competitive with computationally more complex methods such as maximum-likelihood estimation.

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