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ASYMPTOTIC DEPENDENCE BETWEEN RANDOM CENTRAL QUASI-RANGES AND RANDOM EMPIRICAL QUANTILES
Nigm, E.M. 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.1
The asymptotic dependence between the central quasi-ranges and empirical quantiles was studied. The asymptotic dependence are obtained when the sample size is a positive integer valued random variable (r. v.). The dependence conditions and limit forms are obtained under generl conditions such as : the interrelation of the basic variables (the original random sample) and the random sample size is not restricted. In additition the normalizing constants do not depend on the random size.
Asymptotic dependence between random central quasi-ranges and random empirical quantiles
E. M. Nigm 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-
The asymptotic dependence between the central quasi-ranges and empirical quantiles was studied. The asymptotic dependence are obtained when the sample size is a positive integer valued random variable (r.v.). The dependence conditions and limit forms are obtained under generl conditions such as : the interrelation of the basic variables (the original random sample) and the random sample size is not restricted. In additition the normalizing constants do not depend on the random size.
CONTINUATION THEOREMS OF THE EXTREMES UNDER POWER NORMALIZATION
Barakat, H.M.,Nigm, E.M.,El-Adll, M.E. 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.10 No.1
In this paper an important stability property of the extremes under power normalizations is discussed. It is proved that the restricted convergence of the Power normalized extremes on an arbitrary nondegenerate interval implies the weak convergence. Moreover, this implication, in an important practical situation, is obtained when the sample size is considered as a random variable distributed geometrically with mean n.
A NOTE ON THE CONVERGENCE OF TRIVARIATE EXTREME ORDER STATISTICS AND EXTENSION
BARAKAT, H. M.,NIGM, E. M.,ASKAR, M. M. 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1
Necessary and sufficient conditions, under which there exists (at least) a sequence of vectors of real numbers for which the distribution function (d.f.) of any vector of extreme order statistics converges to a non-degenerate limit, are derived. The interesting thing is that these conditions solely depend on the univariate marginals. Moreover, the limit splits into the product of the limit univariate marginals if all the bivariate marginals of the trivariate d.f., from which the sample is drawn, is of negative quadrant dependent random variables (r.v.'s). Finally, all these results are stated for the multivariate extremes with arbitrary dimensions.
A note on the convergence of trivariate extreme orderstatistics and extension
H. M. Barakat,E. M. Nigm,M. M. Askar 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1-2
Necessary and sufficient conditions, under which there exists (at least) a sequence of vectors of real numbers for which the distribution function (d.f.) of any vector of extreme order statistics converges to a nondegenerate limit, are derived. The interesting thing is that these conditions solely depend on the univariate marginals. Moreover, the limit splits into the product of the limit univariate marginals if all the bivariate marginals of the trivariate d.f., from which the sample is drawn, is of negative quadrant dependent random variables (r.v.’s). Finally, all these results are stated for the multivariate extremes with arbitrary dimensions.
Current records and record range with some applications
H. M. Barakat,E.M.NIGM,R.A. Aldallal 한국통계학회 2014 Journal of the Korean Statistical Society Vol.43 No.2
In a sequence of independent and identically distributed (iid) random variables, theupper (lower) current records and record range are studied. We derive general recurrencerelations between the single and product moments for the upper and lower currentrecords based on Weibull and positive Weibull distributions, as well as Pareto and negativePareto distributions, respectively. Moreover, some asymptotic results for general currentrecords are established. In addition, a recurrence relation and an explicit formula forthe moments of record range based on the exponential distribution are given. Finally,numerical examples are presented to illustrate and corroborate theoretical results.