JSM 2004 - Toronto

Abstract #301407

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Activity Number: 408
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #301407
Title: A Modeling Approach for Distributions with Parametric Tails
Author(s): Jin Cao*+ and Yongzhao Shao
Companies: Bell Labs Lucent Technologies and New York University
Address: 700 Mountain Ave., Murray Hill, NJ, 07974,
Keywords: parametric tail ; Pareto ; Moran's statistic ; semiparametric ; communication networks ; sample spacings
Abstract:

Many datasets can be modeled by a distribution with a known parametric tail. For example, the web file sizes in communication networks have heavy tails, and thus the tail is often modelled by a Pareto distribution. To make inference on such a distribution (e.g., estimating its mean), we propose to use a semiparametric model where the distribution is modeled nonparametrically with a tail from a known parametric family f(x;\theta). We propose an estimator that are used to determine both the starting point of the parametric tail and the possibly unknown parameter value \theta simultaneously based on the method of spacings and establish its consistency property under general conditions. We illustrate our modeling approach using a real dataset of web file sizes.

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