On an inequality of Karlin and Rinott concerning weighted sums of i.i.d. random variables

Yu, Yaming

doi:10.1017/s0001867800003037

Cited by 5 publications

(2 citation statements)

References 11 publications

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“…The proof of Theorem 1 is facilitated by a key lemma, the basic idea of which dates back to Karlin and Rinott [14]; see [31] for a continuous version, and see [32] for an application analyzing the monotonicity of entropy in a special Poisson limit theorem.…”

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confidence: 99%

On the Entropy of Compound Distributions on Nonnegative Integers

2009

IEEE Trans. Inform. Theory

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Section: Definitionmentioning

confidence: 99%

On the Entropy of Compound Distributions on Nonnegative Integers

2009

IEEE Trans. Inform. Theory

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“…The motivation in the last three papers, and numerous others, is the performance of some wireless systems that depends on the coefficients of the linear combination Q. For stochastic comparisons between such linear combinations see Yu (2008Yu ( , 2011 and references therein.…”

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A Colonel Blotto Gladiator Game

Rinott

Scarsini

2012

SSRN Journal

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We consider a stochastic version of the well-known Blotto game, called the gladiator game. In this zero-sum allocation game two teams of gladiators engage in a sequence of one-to-one fights in which the probability of winning is a function of the gladiators' strengths. Each team's strategy consist the allocation of its total strength among its gladiators. We find the Nash equilibria and the value of this class of games and show how they depend on the total strength of teams and the number of gladiators in each team. To do this, we study interesting majorization-type probability inequalities concerning linear combinations of Gamma random variables. Similar inequalities have been used in models of telecommunications and research and development.

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Ranking Forecasts by Stochastic Error Distance, Information and Reliability Measures

Ardakani

Ebrahimi

Soofi

2018

Int Statistical Rev

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The stochastic error distance (SED) introduced by Diebold and Shin (2017) ranks forecast models by divergence between distributions of the errors of the actual and perfect forecast models. The basic SED is defined by the variation distance and provides a representation of the mean absolute error, but by basing ranking on the entire error distribution and divergence, the SED moves beyond the traditional forecast evaluations. First, we establish connections between ranking forecast models by the SED, error entropy and some partial orderings of distributions. Then, we introduce the notion of excess error for forecast errors of magnitudes larger than a tolerance threshold and give the SED representation of the mean excess error (MEE). As a function of the threshold, the MEE is a local risk measure. With the distribution of the absolute error as a prior for the threshold, its Bayes risk is the entropy functional of the survival function, which is a known measure in the information theory and reliability. Notions and results are illustrated using various distributions for the error. The empirical versions of SED, MEE and its Bayes risk are compared with the mean squared error in ranking regression and autoregressive integrated moving average models for forecasting bond risk premia.

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On an inequality of Karlin and Rinott concerning weighted sums of i.i.d. random variables

Cited by 5 publications

References 11 publications

On the Entropy of Compound Distributions on Nonnegative Integers

On the Entropy of Compound Distributions on Nonnegative Integers

A Colonel Blotto Gladiator Game

Ranking Forecasts by Stochastic Error Distance, Information and Reliability Measures

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