On A General System of Distributions I. Its Curve-Shape Characteristics II. The Sample Median

Burr, Irving W.; Cislak, Peter J.

doi:10.1080/01621459.1968.11009281

Cited by 58 publications

(43 citation statements)

References 14 publications

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“…One member of the family, the Burr XII distribution, has found application in many areas (Lindsay et al 1996;Wang et al 1996;Wingo 1993). The properties of the Burr XII distribution and relations between this distribution and other distributions were investigated by Burr and Cislak (1968), Rodriguez (1977), and Tadikamalla (1980). Shao et al (2004) developed an extended three-parameter Burr XII distribution and applied it to flood frequency analysis.…”

Section: Introductionmentioning

confidence: 98%

Entropy-based parameter estimation for extended Burr XII distribution

Hao

Singh

2008

Stoch Environ Res Risk Assess

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Two entropy-based methods, called ordinary entropy (ENT) method and parameter space expansion method (PSEM), both based on the principle of maximum entropy, are applied for estimating parameters of the extended Burr XII distribution. With the parameters so estimated, the extended Burr XII distribution is applied to six peak flow datasets and quantiles (discharges) corresponding to different return periods are computed. These two entropy methods are compared with the methods of moments (MOM), probability weighted moments (PWM) and maximum likelihood estimation (MLE). It is shown that PSEM yields the same quantiles as does MLE for discrete cases, while ENT is found comparable to the MOM and PWM. For shorter return periods (\10-30 years), quantiles (discharges) estimated by these four methods are in close agreement, but the differences amongst them grow as the return period increases. The error in quantiles computed using the four methods becomes larger for return periods greater than 10-30 years.

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Section: Introductionmentioning

confidence: 98%

Entropy-based parameter estimation for extended Burr XII distribution

Hao

Singh

2008

Stoch Environ Res Risk Assess

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“…We cannot answer this question completely, but we can get close to it by studying the Burr (or Singh-Maddala) distribution (Burr 1942;Burr and Cislak 1968), defined as…”

Section: Bounded Utilitymentioning

confidence: 99%

Pareto utility

et al. 2012

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In searching for an appropriate utility function in the expected utility framework, we formulate four properties that we want the utility function to satisfy. We conduct a search for such a function, and we identify Pareto utility as a function satisfying all four desired properties. Pareto utility is a flexible yet simple and parsimonious two-parameter family. It exhibits decreasing absolute risk aversion and increasing but bounded relative risk aversion. It is applicable irrespective of the probability distribution relevant to the prospect to be evaluated. Pareto utility is therefore particularly suited for catastrophic risk analysis. A new and related class of generalized exponential (gexpo) utility functions is also studied. This class is particularly relevant in situations where absolute risk tolerance is thought to be concave rather than linear.

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“…Both functions are members of the HARA class of utility functions. The Burr function, based on Burr (1942) and Burr and Cislak (1968), was proposed in Ikefuji et al (2010b), where it is also shown that this function is particularly appropriate as an approximation to a bounded utility function and enjoys a combination of appealing properties especially relevant in heavy-tailed risk analysis. This is exemplified in Figure 3, where we plot RRA and ARA for The parameter choice is determined by the point x * , where we want the three functions to be close.…”

Section: Compatibility: Non-normality and Burr Utilitymentioning

confidence: 99%

Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model

Ikefuji

Laeven

Muris³

et al. 2010

SSRN Journal

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Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate ModelIkefuji, M.; Laeven, R.J.A.; Magnus, J.R.; Müris, C.H.M. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policyIf you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. Chris MurisCentER, Tilburg University * We are grateful to Graciela Chichilnisky, John Einmahl, Reyer Gerlagh, Johan Eyckmans, Sjak Smulders, Peter Wakker, Aart de Zeeuw, Amos Zemel, and seminar participants at the Tilburg Sustainability Center for helpful comments. This research was funded in part by the JSPS under grant C-22530177 (Ikefuji) and by the NWO under grant Vidi-2009 (Laeven). E-mail addresses: ikefuji@iser.osaka-u.ac.jp (Ikefuji), r.j.a.laeven@uvt.nl (Laeven), magnus@uvt.nl (Magnus), chrismuris@gmail.com (Muris). Abstract: In the context of extreme climate change, we ask how to conduct expected utility analysis in the presence of catastrophic risks. Economists typically model decision making under risk and uncertainty by expected utility with constant relative risk aversion (power utility); statisticians typically model economic catastrophes by probability distributions with heavy tails. Unfortunately, the expected utility framework is fragile with respect to heavy-tailed distributional assumptions. We specify a stochastic economyclimate model with power utility and explicitly demonstrate this fragility. We derive necessary and sufficient compatibility conditions on the utility function to avoid fragility and solve our stochastic economy-climate model for two examples of such compatible utility functions. We further develop and implement a procedure to learn the input parameters of our model and show that the model thus specified produces quite robust optimal policies. The numerical results indicate that higher levels of uncertainty (heavier tails) lead to less abatement and consumption, and to more investment, but this effect is not unlimited.JEL Classification: D81; Q5.

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On A General System of Distributions I. Its Curve-Shape Characteristics II. The Sample Median

Cited by 58 publications

References 14 publications

Entropy-based parameter estimation for extended Burr XII distribution

Entropy-based parameter estimation for extended Burr XII distribution

Pareto utility

Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model

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