Characterization of the exponential distribution function by Properties of the differenceX k+s∶n−X k∶n of order statistics

Riedel, M.; Rossberg, Hans-Joachim

doi:10.1007/bf01895297

Cited by 15 publications

(15 citation statements)

References 5 publications

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“…given by Riedel-Rossberg characterization in terms of order statistics, see [90]. Denote, as usually, by X k,n the k-th order statistic in the sample of size n, 1 ≤ k ≤ n. Then the following characterization holds.…”

Section: Characterizations Based On Order Statistics Another Example Ismentioning

confidence: 99%

Tests based on characterizations, and their efficiencies: a survey

Nikitin

2017

ACUTM

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Abstract. A survey of goodness-of-fit and symmetry tests based on the characterization properties of distributions is presented. This approach became popular in recent years. In most cases the test statistics are functionals of U -empirical processes. The limiting distributions and large deviations of new statistics under the null hypothesis are described. Their local Bahadur efficiency for various parametric alternatives is calculated and compared with each other as well as with diverse previously known tests. We also describe new directions of possible research in this domain.

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Section: Characterizations Based On Order Statistics Another Example Ismentioning

confidence: 99%

Tests based on characterizations, and their efficiencies: a survey

Nikitin

2017

ACUTM

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“…The characterization holds true under some additional technical and rather unfriendly conditions; see e.g. Riedel & Rossberg (1994) or Rossberg, Riedel & Ramachandran (1997). It appears that our results on power distributions lead to characterizing the exponential law by equidistribution of X k+1: n and X k: n + W, where W is an independent exponential rv -which looks rather unexpected in view of Rossberg's counter-example.…”

Section: Introductionmentioning

confidence: 96%

Switching Order Statistics through Random Power Contractions

Wesołowski

Ahsanullah

2004

Aus NZ J of Statistics

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This paper investigates a new random contraction scheme which complements the lengthbiasing and convolution contraction schemes considered in the literature. A random power contraction is used with order statistics, leading to new and elegant characterizations of the power distribution. In view of Rossberg's counter-example of a non-exponential law with exponentially distributed spacings of order statistics, possibly the most appealing consequence of the result is a characterization of the exponential distribution via an independent exponential shift of order statistics.

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“…Scaling law-like expressions are needed to estimate the performance of the next generation of experimental fusion machines. While much effort has been spent on generating scaling laws for performance parameters, only the Ohmic temperature profile shapes have been parameterised in terms of the engineering variables [1,2,3] . In this article, we report the results of the parameterisation of the Joint European Torus [4] (JET) electron temperature profiles and density shapes for different confinement regimes.…”

Section: Introductionmentioning

confidence: 99%

“…We use the log additive models of Refs. [1,2,3] to represent the profiles in terms of the normalised toroidal flux radius, ρ, and the engineering control variables such as q 95 , I p , P L , etc. The log-additive model is essentially a scaling expression for profile shapes:…”

Section: Introductionmentioning

confidence: 99%

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Profile shape parameterization of JET electron temperature and density profiles

Schunke

Imre²,

Riedel³

1997

Nucl. Fusion

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The temperature and density profiles of the Joint European Torus are parameterised using log-additive models in the control variables. Predictive error criteria are used to determine which terms in the log-linear model to include. The density and temperature profiles are normalised to their line averages (n and T ). The normalised Ohmic density shape depends primarily on the parameter n/B t , where B t is the toroidal magnetic field. Both the Low-mode (L-mode) and edge localized mode-free (ELM-free) high mode (H-mode) temperature profile shapes depend strongly on the type of heating power, with ion cyclotron resonant heating producing a more peaked profile than neutral beam injection. Given the heating type dependence, the L-mode temperature shape is nearly independent of the other control variables. The H-mode temperature shape broadens as the effective charge, Z ef f , increases. The line average L-mode temperature scales as B .96 t (Power per particle) .385 . The L-mode normalised density shape depends primarily on the ratio of line average density, n, to the edge safety factor, q 95 . As n/q 95 increases, the profile shape broadens. The current, I p , is the most important control variable for the normalised Hmode density. As the current increases, the profile broadens and the gradient at the edge sharpens. Increasing the heating power, especially the ion cyclotron resonant heating, or decreasing the average density, peaks the H-mode density profile slightly.

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Characterization of the exponential distribution function by Properties of the differenceX k+s∶n−X k∶n of order statistics

Abstract: We consider n independent and identically distributed random variables with common continuous distribution function F concentrated on (0, oo).

Cited by 15 publications

References 5 publications

Tests based on characterizations, and their efficiencies: a survey

Tests based on characterizations, and their efficiencies: a survey

Switching Order Statistics through Random Power Contractions

Profile shape parameterization of JET electron temperature and density profiles

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