A Guide to the Burr Type XII Distributions

Rodriguez, Robert N.

doi:10.2307/2335782

Cited by 35 publications

(34 citation statements)

References 5 publications

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“…It has also been applied to the analysis of the duration of volcanic eruptions (Gunn et al, 2013) and the modelling of irregularities in tree diameter (Tsogt and Lin, 2012). The Burr Type XII distribution also includes other distributions as special cases, for example the Lognormal, Gamma or Pareto Type II distribution and has the Weibull distribution as a limiting case (Rodriguez, 1977). So it is clearly the most flexible out of the three distributions considered in this study.…”

Section: The Burr XII Distributionmentioning

confidence: 99%

Quantifying catastrophic and climate impacted hazards based on local expert opinions

Keighley

Longden

Mathew

et al. 2018

Journal of Environmental Management

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The analysis of catastrophic and climate impacted hazards is a challenging but important exercise, as the occurrence of such events is usually associated with high damage and uncertainty. Often, at the local level, there is a lack of information on rare extreme events, such that available data is not sufficient to fit a distribution and derive parameter values for the frequency and severity distributions. This paper discusses local assessments of extreme events and examines the potential of using expert opinions in order to obtain values for the distribution parameters. In particular, we illustrate a simple approach, where a local expert is required to only specify two percentiles of the loss distribution in order to provide an estimate for the severity distribution of climate impacted hazards. In our approach, we focus on so-called heavy-tailed distributions for the severity, such as the Lognormal, Weibull and Burr XII distribution. These distributions are widely used to fit data from catastrophic events and can also represent extreme losses or the so-called tail of the distribution. An illustration of the method is provided utilising an example that quantifies the risk of bushfires in a local area in Northern Sydney.

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Section: The Burr XII Distributionmentioning

confidence: 99%

Quantifying catastrophic and climate impacted hazards based on local expert opinions

Keighley

Longden

Mathew

et al. 2018

Journal of Environmental Management

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“…The Burr Type XII family (Rodriguez (1977)) has two shape parameters, c, k > 0, with the rth raw moment μ r = Γ(r/c + 1)Γ(k − r/c)/Γ(k), c > 0, k > 0, r < ck. The regime in the (γ 2 , γ 3 ) plane is bounded below by the curve corresponding to the Weibull family (rth raw moment μ r = Γ(r/c + 1), where c > 0 is the Weibull shape parameter), and above by the curve…”

Section: Appendixmentioning

confidence: 99%

“…23, 390). Rodriguez (1977), in clarifying the region occupied by the Burr Type XII distribution in relation to others, provides a fairly comprehensive version of the moment-ratio diagram showing several important regions. Tadikamalla (1980) provides a similar but limited version in clarifying the region occupied by the Burr Type III region.…”

Section: Introductionmentioning

confidence: 99%

Moment-Ratio Diagrams for Univariate Distributions

Vargo

Pasupathy

Leemis

2016

International Series in Operations Research &Amp; Management Science

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We present two moment-ratio diagrams along with guidance for their interpretation. The first momentratio diagram is a graph of skewness versus kurtosis for common univariate probability distributions. The second moment-ratio diagram is a graph of coefficient of variation versus skewness for common univariate probability distributions. Both of these diagrams, to our knowledge, are the most comprehensive to date. The diagrams serve four purposes: (1) they quantify the proximity between various univariate distributions based on their second, third, and fourth moments; (2) they illustrate the versatility of a particular distribution based on the range of values that the various moments can assume; and (3) they can be used to create a short list of potential probability models based on a data set; (4) they clarify the limiting relationships between various well-known distribution families. The use of the moment-ratio diagrams for choosing a distribution that models given data is illustrated.

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“…Zimmer et al (1998) discussed the statistical and probabilistic properties of the Burr Type-XII distribution and its relationship to other distributions used in reliability analyses. Rodriguez (1977) presented complete guides about the Burr Type-XII distributions. Lots of work has done on underlying distribution, a little few of them are discussed here.…”

Section: Introductionmentioning

confidence: 99%

Progressive Censored Burr Type-XII Distribution Under Random Removal Scheme: Some Inferences

Prakash¹

2017

JAS

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Abstract. When some sample values at either or both the extremes might have been assorted, a censoring scheme is much useful. Nevertheless, in some reliability experiments, the number of items fell out the experiment cannot be prefixed random in some situations. For such situations, a random removal scheme with censoring scheme may offer a good result. Here, a random removal scheme with the Progressive censoring plan is assumed for statistical inference, when fill out items of the experiments cannot be prefixed. The analysis of the present discussion has carried out with the help of a real data set for the Burr Type-XII distribution.Résumé. Lorsque certaines valeurs d'échantillonà l'une ou l'autre des deux extrêmes ont puêtre assorties, un schéma de censure est très utile. Néanmoins, dans certaines expériences de fiabilité, le nombre d'articles tombés en panne ne peut pasêtre préfixé. Dans de telles situations, un système de suppression aléatoire avec un système de censure peut offrir un bon résultat. Ici, un système de suppression aléatoire avec un plan de censure progressif est supposé pour l'inférence statistique, lorsque le nombre de pannes ne peutêtre préfixé. L'analyse de la présente discussion aété effectuéeà l'aide d'un ensemble de données réelles issues de la distribution Burr Type-XII.

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A Guide to the Burr Type XII Distributions

Cited by 35 publications

References 5 publications

Quantifying catastrophic and climate impacted hazards based on local expert opinions

Quantifying catastrophic and climate impacted hazards based on local expert opinions

Moment-Ratio Diagrams for Univariate Distributions

Progressive Censored Burr Type-XII Distribution Under Random Removal Scheme: Some Inferences

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