Tailweight, Statistical Inference and Families of Distributions — A Brief Survey
There are surprisingly many concepts and definitions of tailweight. For symmetric distributions F and G the main results are based on the convexity or starshapedness of G -1F. This has essentially replaced kurtosis as measure of tailweight. Recently in research on the location problem there has been interest in families of distributions ordered by tailweight and in statistical procedures for assessing tailweight. This problem of assessing tailweight has long been a problem of interest to researchers developing life models. There is a rich variety of results for testing the exponential family against an alternative with lighter tails. Hopefully, there will soon be an equally rich variety of results for testing the tails of a symmetric distribution in the location model.
Key WordsTailweight symmetric distributions life models convex and starshaped functions
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