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A comparative study of lognormal, gamma and beta modelling in radon mapping with recommendations regarding bias, sample sizes and the treatment of outliers.

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Title: A comparative study of lognormal, gamma and beta modelling in radon mapping with recommendations regarding bias, sample sizes and the treatment of outliers.
Authors: Patrick Murphy, Catherine Organo
Source: Journal of Radiological Protection. Sep2008, Vol. 28 Issue 3, p293-302. 10p.
Subjects: Radon, Comparative studies, Lognormal distribution, Beta functions, Statistical sampling, Mathematical models
Geographic Terms: Ireland
Abstract: Radon risk maps have been produced in many countries using non-geologically based techniques utilising the lognormal and gamma distributions to display point estimates of the probability, PRL, that indoor radon levels will exceed a reference level. Recent work on updating radon maps in Ireland prompted an examination of various statistical issues associated with non-geologically based radon mapping techniques. The purpose of this paper is to compare existing techniques with a new theoretically unbiased model which uses the beta distribution to estimate PRL. We examine this new beta based model and four existing models for bias using simulated test data sets. Producing confidence intervals for PRL, we also analyse the relationship between sample size and estimation error for each model and finally we consider the effect of extreme values on estimation procedures. We demonstrate that, under the assumption of lognormally distributed data with outliers, a two stage approach to testing which first detects and removes outliers from the data and then applies the beta based method is most satisfactory from both a theoretical and empirical perspective. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Radiological Protection is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 34034267
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Data: A comparative study of lognormal, gamma and beta modelling in radon mapping with recommendations regarding bias, sample sizes and the treatment of outliers.
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  Data: <searchLink fieldCode="AR" term="%22Patrick+Murphy%22">Patrick Murphy</searchLink><br /><searchLink fieldCode="AR" term="%22Catherine+Organo%22">Catherine Organo</searchLink>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Radiological+Protection%22">Journal of Radiological Protection</searchLink>. Sep2008, Vol. 28 Issue 3, p293-302. 10p.
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  Data: <searchLink fieldCode="DE" term="%22Radon%22">Radon</searchLink><br /><searchLink fieldCode="DE" term="%22Comparative+studies%22">Comparative studies</searchLink><br /><searchLink fieldCode="DE" term="%22Lognormal+distribution%22">Lognormal distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Beta+functions%22">Beta functions</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+sampling%22">Statistical sampling</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Ireland%22">Ireland</searchLink>
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  Label: Abstract
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  Data: Radon risk maps have been produced in many countries using non-geologically based techniques utilising the lognormal and gamma distributions to display point estimates of the probability, PRL, that indoor radon levels will exceed a reference level. Recent work on updating radon maps in Ireland prompted an examination of various statistical issues associated with non-geologically based radon mapping techniques. The purpose of this paper is to compare existing techniques with a new theoretically unbiased model which uses the beta distribution to estimate PRL. We examine this new beta based model and four existing models for bias using simulated test data sets. Producing confidence intervals for PRL, we also analyse the relationship between sample size and estimation error for each model and finally we consider the effect of extreme values on estimation procedures. We demonstrate that, under the assumption of lognormally distributed data with outliers, a two stage approach to testing which first detects and removes outliers from the data and then applies the beta based method is most satisfactory from both a theoretical and empirical perspective. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Radiological Protection is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1088/0952-4746/28/3/001
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      – Code: eng
        Text: English
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        PageCount: 10
        StartPage: 293
    Subjects:
      – SubjectFull: Radon
        Type: general
      – SubjectFull: Comparative studies
        Type: general
      – SubjectFull: Lognormal distribution
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      – SubjectFull: Beta functions
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      – SubjectFull: Statistical sampling
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      – SubjectFull: Mathematical models
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      – SubjectFull: Ireland
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              M: 09
              Text: Sep2008
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              Y: 2008
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