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Displaying similar documents to “Optimal mean-variance bounds on order statistics from families determined by star ordering”

Sharp bounds for expectations of spacings from decreasing density and failure rate families

Katarzyna Danielak, Tomasz Rychlik (2004)

Applicationes Mathematicae

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We apply the method of projecting functions onto convex cones in Hilbert spaces to derive sharp upper bounds for the expectations of spacings from i.i.d. samples coming from restricted families of distributions. Two families are considered: distributions with decreasing density and with decreasing failure rate. We also characterize the distributions for which the bounds are attained.

Evaluations of expected generalized order statistics in various scale units

Erhard Cramer, Udo Kamps, Tomasz Rychlik (2002)

Applicationes Mathematicae

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We present sharp upper bounds for the deviations of expected generalized order statistics from the population mean in various scale units generated by central absolute moments. No restrictions are imposed on the parameters of the generalized order statistics model. The results are derived by combining the unimodality property of the uniform generalized order statistics with the Moriguti and Hölder inequalities. They generalize evaluations for specific models of ordered observations. ...

A note on order statistics from symmetrically distributed samples

Marek Kałuszka, Andrzej Okolewski (2011)

Applicationes Mathematicae

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We present a first moment distribution-free bound on expected values of L-statistics as well as properties of some numerical characteristics of order statistics, in the case when the observations are possibly dependent symmetrically distributed about the common mean. An actuarial interpretation of the presented bound is indicated.

Moments of order statistics of the Generalized T Distribution

Ali İ. Genç (2015)

Discussiones Mathematicae Probability and Statistics

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We derive an explicit expression for the single moments of order statistics from the generalized t (GT) distribution. We also derive an expression for the product moment of any two order statistics from the same distribution. Then the location-scale estimating problem of a real data set is solved alternatively by the best linear unbiased estimates which are based on the moments of order statistics.

Characterizations of the distribution of the Demmel condition number of real Wishart matrices

M. Shakil, M. Ahsanullah (2016)

Special Matrices

Similarity:

The Demmel condition number is an indicator of the matrix condition, and its properties have recently found applications in many practical problems, such as in MIMO communication systems, in the analytical prediction of level-crossing and fade duration statistics of Rayleigh channels, and in spectrum sensing for cognitive radio systems, among others. As the characterizations of a probability distribution play an important role in probability and statistics, in this paper we study the...

Five Turning Points in the Historical Progress of Statistics - My Personal Vision

von Collani, Elart (2014)

Serdica Journal of Computing

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Statistics has penetrated almost all branches of science and all areas of human endeavor. At the same time, statistics is not only misunderstood, misused and abused to a frightening extent, but it is also often much disliked by students in colleges and universities. This lecture discusses/covers/addresses the historical development of statistics, aiming at identifying the most important turning points that led to the present state of statistics and at answering the questions “What went...

A note on optimal probability lower bounds for centered random variables

Mark Veraar (2008)

Colloquium Mathematicae

Similarity:

We obtain lower bounds for ℙ(ξ ≥ 0) and ℙ(ξ > 0) under assumptions on the moments of a centered random variable ξ. The estimates obtained are shown to be optimal and improve results from the literature. They are then applied to obtain probability lower bounds for second order Rademacher chaos.