Distribution of minimum path

1975 ◽  
Vol 12 (1) ◽  
pp. 164-166
Author(s):  
Aaron Tenenbein
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Random Variables ◽  
The Other ◽  
Minimum Path

Let Y, X1, X2, …, Xn be a set of n + 1 independently and uniformly distributed random variables on the interval (0, 1). The distribution of the length of the minimum path starting at Y which covers the other n points is derived. The solution is interesting in that it involves finding the distribution of an order statistic of a function of order statistics.

Distribution of minimum path

1975 ◽  
Vol 12 (01) ◽  
pp. 164-166
Author(s):  
Aaron Tenenbein
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Random Variables ◽  
The Other ◽  
Minimum Path

Let Y, X 1, X 2, …, Xn be a set of n + 1 independently and uniformly distributed random variables on the interval (0, 1). The distribution of the length of the minimum path starting at Y which covers the other n points is derived. The solution is interesting in that it involves finding the distribution of an order statistic of a function of order statistics.

scholarly journals A Note on Conditioning and Stochastic Domination for Order Statistics

2008 ◽  
Vol 45 (2) ◽  
pp. 575-579 ◽  
Author(s):  
Devdatt Dubhashi ◽  
Olle Häggström
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Conditional Distribution ◽  
Random Variables ◽  
Stochastic Domination

For an order statistic (X1:n,…,Xn:n) of a collection of independent but not necessarily identically distributed random variables, and any i ∈ {1,…,n}, the conditional distribution of (Xi+1:n,…,Xn:n) given Xi:n > s is shown to be stochastically increasing in s. This answers a question by Hu and Xie (2006).

scholarly journals Complete convergence for arrays of ratios of order statistics

2019 ◽  
Vol 17 (1) ◽  
pp. 439-451
Author(s):  
Yu Miao ◽  
Huanhuan Ma ◽  
Shoufang Xu ◽  
Andre Adler
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Complete Convergence ◽  
Pareto Distribution ◽  
Random Variables ◽  
Independent Random Variables

Abstract Let {Xn,k, 1 ≤ k ≤ mn, n ≥ 1} be an array of independent random variables from the Pareto distribution. Let Xn(k) be the kth largest order statistic from the nth row of the array and set Rn,in,jn = Xn(jn)/Xn(in) where jn < in. The aim of this paper is to study the complete convergence of the ratios {Rn,in,jn, n ≥ 1}.

EQUIVALENT CHARACTERIZATIONS ON ORDERINGS OF ORDER STATISTICS AND SAMPLE RANGES

2010 ◽  
Vol 24 (2) ◽  
pp. 245-262 ◽  
Author(s):  
Tiantian Mao ◽  
Taizhong Hu
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Geometric Distribution ◽  
Random Variables ◽  
The Other ◽  
Stochastic Orders ◽  
Exponential Random Variables ◽  
Discrete Counterpart ◽  
Similarities And Differences ◽  
Geometric Variables

The purpose of this article is to present several equivalent characterizations of comparing the largest-order statistics and sample ranges of two sets of n independent exponential random variables with respect to different stochastic orders, where the random variables in one set are heterogeneous and the random variables in the other set are identically distributed. The main results complement and extend several known results in the literature. The geometric distribution can be regarded as the discrete counterpart of the exponential distribution. We also study the orderings of the largest-order statistics from geometric random variables and point out similarities and differences between orderings of the largest-order statistics from geometric variables and from exponential variables.

scholarly journals On order statistics from nonidentical discrete random variables

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 192-196
Author(s):  
Bahadır Yüzbaşı ◽  
Yunus Bulut ◽  
Mehmet Güngör
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Random Variables ◽  
Integral Form ◽  
Discrete Case ◽  
Discrete Random Variables

AbstractIn this study, pf and df of single order statistic of nonidentical discrete random variables are obtained. These functions are also expressed in integral form. Finally, pf and df of extreme of order statistics of random variables for the nonidentical discrete case are given.

scholarly journals ON STOCHASTIC COMPARISONS OF ORDER STATISTICS FROM HETEROGENEOUS EXPONENTIAL SAMPLES

2019 ◽  
pp. 1-6
Author(s):  
Yaming Yu
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Open Problem ◽  
Hazard Rate ◽  
Random Variables ◽  
Stochastic Comparisons ◽  
Heterogeneous Sample ◽  
Exponential Random Variables ◽  
Hazard Rate Ordering

Abstract We show that the kth order statistic from a heterogeneous sample of n ≥ k exponential random variables is larger than that from a homogeneous exponential sample in the sense of star ordering, as conjectured by Xu and Balakrishnan [14]. As a consequence, we establish hazard rate ordering for order statistics between heterogeneous and homogeneous exponential samples, resolving an open problem of Pǎltǎnea [11]. Extensions to general spacings are also presented.

scholarly journals OPTIMAL MOMENT INEQUALITIES FOR ORDER STATISTICS FROM NONNEGATIVE RANDOM VARIABLES

2019 ◽  
pp. 1-15
Author(s):  
Nickos Papadatos
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Random Variables ◽  
Upper Bounds ◽  
Moment Inequalities ◽  
Population Mean ◽  
Sample Minimum ◽  
Independent Identically Distributed

We obtain the best possible upper bounds for the moments of a single-order statistic from independent, nonnegative random variables, in terms of the population mean. The main result covers the independent identically distributed case. Furthermore, the case of the sample minimum for merely independent (not necessarily identically distributed) random variables is treated in detail.

scholarly journals A Note on Conditioning and Stochastic Domination for Order Statistics

2008 ◽  
Vol 45 (02) ◽  
pp. 575-579
Author(s):  
Devdatt Dubhashi ◽  
Olle Häggström
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Conditional Distribution ◽  
Random Variables ◽  
Stochastic Domination

For an order statistic (X 1:n ,…,X n:n ) of a collection of independent but not necessarily identically distributed random variables, and any i ∈ {1,…,n}, the conditional distribution of (X i+1:n ,…,X n:n ) given X i:n &gt; s is shown to be stochastically increasing in s. This answers a question by Hu and Xie (2006).

A Note on the Accuracy of Normal Approximation of Random Quantities

2021 ◽  
Vol 73 (1) ◽  
pp. 62-67
Author(s):  
Ibrahim A. Ahmad ◽  
A. R. Mugdadi
Keyword(s):  
Sample Size ◽  
Order Statistic ◽  
Normal Approximation ◽  
Order Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Limiting Distribution ◽  
Exact Order ◽  
Fixed Sample ◽  
Independent Identically Distributed

For a sequence of independent, identically distributed random variable (iid rv's) [Formula: see text] and a sequence of integer-valued random variables [Formula: see text], define the random quantiles as [Formula: see text], where [Formula: see text] denote the largest integer less than or equal to [Formula: see text], and [Formula: see text] the [Formula: see text]th order statistic in a sample [Formula: see text] and [Formula: see text]. In this note, the limiting distribution and its exact order approximation are obtained for [Formula: see text]. The limiting distribution result we obtain extends the work of several including Wretman[Formula: see text]. The exact order of normal approximation generalizes the fixed sample size results of Reiss[Formula: see text]. AMS 2000 subject classification: 60F12; 60F05; 62G30.

Stochastic comparisons of order statistics under multivariate imperfect repair

1996 ◽  
Vol 33 (1) ◽  
pp. 156-163 ◽  
Author(s):  
Taizhong Hu
Keyword(s):  
Order Statistics ◽  
Probability Space ◽  
Random Variables ◽  
Stochastic Comparisons ◽  
Special Model ◽  
Imperfect Repair ◽  
Monotone Coupling ◽  
Common Probability

A monotone coupling of order statistics from two sets of independent non-negative random variables Xi, i = 1, ···, n, and Yi, i = 1, ···, n, means that there exist random variables X′i, Y′i, i = 1, ···, n, on a common probability space such that , and a.s. j = 1, ···, n, where X(1) ≦ X(2) ≦ ·· ·≦ X(n) are the order statistics of Xi, i = 1, ···, n (with the corresponding notations for the X′, Y, Y′ sample). In this paper, we study the monotone coupling of order statistics of lifetimes in two multi-unit systems under multivariate imperfect repair. Similar results for a special model due to Ross are also given.

Sign in / Sign up

Export Citation Format

Share Document