{"title":"The Performance of the Maximum Likelihood Estimator for the Bell Distribution for Count Data","authors":"David E. Giles","doi":"10.56801/jmasm.v23.i2.3","DOIUrl":null,"url":null,"abstract":"The single-parameter “Bell distribution” for discrete data allows for over-dispersion in the data. The maximum likelihood estimator for its parameter is downward-biased in finite samples. We consider various methods for reducing this bias. A simulation study shows that these are effective and also lead to a small improvement in the mean squared error of the estimator. The Cox-Snell correction is the recommended. choice among the options that are considered.","PeriodicalId":47201,"journal":{"name":"Journal of Modern Applied Statistical Methods","volume":"67 9","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Modern Applied Statistical Methods","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56801/jmasm.v23.i2.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
The single-parameter “Bell distribution” for discrete data allows for over-dispersion in the data. The maximum likelihood estimator for its parameter is downward-biased in finite samples. We consider various methods for reducing this bias. A simulation study shows that these are effective and also lead to a small improvement in the mean squared error of the estimator. The Cox-Snell correction is the recommended. choice among the options that are considered.
期刊介绍：
The Journal of Modern Applied Statistical Methods is an independent, peer-reviewed, open access journal designed to provide an outlet for the scholarly works of applied nonparametric or parametric statisticians, data analysts, researchers, classical or modern psychometricians, and quantitative or qualitative methodologists/evaluators.
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