@MISC{Yu13negativeweibull, author = {Kim Yu}, title = {Negative Weibull tail-distributions}, year = {2013} }

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Abstract

We propose a new family of distributions referred to as Weibull taildistributions. This family is designed to model left tails with exponential behavior. The exponent can be estimated using inference procedures adapted from the Weibull tail-distributions literature. Let us define a negative Weibull tail-distribution through its distribution function by: F(x) = exp −(−x) 1/θ} ℓ(−x) , x < 0 (1) where ℓ is a slowly-varying function. Our main result permits to link negative Weibull tail-distributions with classical Weibull tail-distributions, see Table 1 for examples, [23, 21] for stability properties and [20] for a review. A sufficient condition for subexponentiality has been established in [19], Theorem 1. A new diagnostic tool has been proposed in [22]. Theorem. Let X be a random variable from the negative Weibull-tail model (1). Let Y = −X. Then, Y follows a Weibull tail-distribution with associated Weibull tail-coefficient θ. Proof. Let us consider