Order statisticsLaw of large numbersComplete convergenceLarge deviation principleLet $\\{X_{ni}, 1 \\leq i \\leq m_{n}, n\\geq 1\\}$ { X n i , 1 ≤ i ≤ m n , n ≥ 1 } be an array of independent random variables with uniform distribution on $[0, heta _{n}]$ [ 0 ...
Uniform Approximation to Distributions of Extreme Order Statistics This paper deals with asymptotic expansions of the distribution of the kth-largest order statistic Zn-k+1: nfor the sample size n. These expansions establi... Reiss, R.-D. - 《Annals of the Institute of Statistical Mathematics》...
orderstatisticsestimator统计顺序week week 2 1 Order Statistics • The order statistics of a set of random variables X 1 , X 2 ,…, X n are the same random variables arranged in increasing order. • Denote by X (1) = smallest of X 1 , X 2 ,…, X n X (2) = 2 nd smallest...
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We first mention that the arguments presented below are based on some well-known properties of order statistics from exponential random variables (see e.g. [3], or [2], as general reference). Let Fj:n be the distribution function of Xj:n,j=1,…,n. Assume that k∈{1,…,n−1}....
We also show that the variables \\min_{1 \\le k \\le n} \\frac{2n}{k(k+1)} \\sum_{i=1}^k U_{i, n} converge in distribution to V. Here U_{i, n} are the order statistics of n i.i.d. random variables uniformly distributed on [0,1]....
(nKn-logn+log3n)=calmostsurely,where-log2<_c<0,andlog,isthejtimesiteratedlogarithm.l.Introduction.ConsiderasequenceX1,X2,...ofindependentidenticallydistrib-utedrandomvariableswithauniformdistributionon[0,1].IfX(1)aretheorderstatisticscorrespondingtoX1,•••,Xn_1ithenthemaximaluniformspacing(or...
A note on uniform approximation to distributions of extreme order statistics The error bound of an approximation to the distribution of thekth largest order statistic as established by Reiss (1981,Adv. Appl. Prob.,13, 533–547) is i... W Kohne,RD Reiss - 《Annals of the Institute of Stat...
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HealthStatistics EntityHealth EntityHealthState EntityHealthStateChunk EntityHealthStateChunkList Époque EventHealthEvaluation FabricCodeVersionInfo FabricConfigVersionInfo ClusterConfigurationUpgradeStatusInfo Informations sur l’intégrité Int64RangePartitionInformation LoadedPartitionInformationResult LoadedPartitionInforma...