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Let $\mu$ be a probability measure on $\mathbb{R}$ with cumulative distribution function $F$, $(x_{i})_{1}^{n}$ a large i.i.d. sample from $\mu$, and $F_{n}$ the associated empirical distribution func...
Characterisations of the geometric distribution using distributional properties of the order statistics
The domain of attraction of stable laws and extreme order statistics
U-functions of concomitants of order statistics
Let {x, Xd, 1 d j d m., n 3 1) be independent and identically distributed random variables with the Pareto distribution. Let X,,, be the k-th largest order statistic from the n-th row of our array....
As the distribulivn function (dd) of the suitably normalized general intermediate (or central) term of order statistics converges on an interval [c, dl to an arbitrary nondecreasing function, the c...
Let X,, n 2 1, be a sequence of independent and identically distributed rmdom variables and X,,, < X,,, < . . . < X,, denote the order statistics of Xi,.. ., X,. For any sequenoe 01 integers {k,) w...
We present sharp bounds for expectations of generalized order statistics with random indices expressed in terms of Tsallis' entropy. The bounds are attainable and provide new characterizations of s...
We prove almost sure versions of distributional limit theorems for central order statistics. We develop a new method which not only gives a simplified proof of existing results in the literature, bu...
Copula Associated to Order Statistics
The Limiting Copula of the Two Largest Order Statistics of Independent and Identically Distributed Samples
Let $M_{n}^{(k)}$ denote the $k$th largest maximum of a sample $(X_{1},X_{2}, \ldots, X_{n})$ from parent $X$ with continuous distribution. Assume there exist normalizing constants $a_{n}>0$, $b_{n}in...
Consider a set of order statistics that arise from sorting samples from two different populations, each with their own, possibly different distribution function. The probability that these order sta...
The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost o...

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