共查询到20条相似文献,搜索用时 125 毫秒
1.
Kilani Ghoudi Abdelhaq Khoudraji Et Louis-Paul Rivest 《Revue canadienne de statistique》1998,26(1):187-197
Let (X, Y) be a bivariate random vector whose distribution function H(x, y) belongs to the class of bivariate extreme-value distributions. If F1 and F2 are the marginals of X and Y, then H(x, y) = C{F1(x),F2(y)}, where C is a bivariate extreme-value dependence function. This paper gives the joint distribution of the random variables Z = {log F1(X)}/{log F1(X)F2(Y)} and W = C{F1{(X),F2(Y)}. Using this distribution, an algorithm to generate random variables having bivariate extreme-value distribution is présentés. Furthermore, it is shown that for any bivariate extreme-value dependence function C, the distribution of the random variable W = C{F1(X),F2(Y)} belongs to a monoparametric family of distributions. This property is used to derive goodness-of-fit statistics to determine whether a copula belongs to an extreme-value family. 相似文献
2.
Let X1,., Xn, be i.i.d. random variables with distribution function F, and let Y1,.,.,Yn be i.i.d. with distribution function G. For i = 1, 2,.,., n set δi, = 1 if Xi ≤ Yi, and 0 otherwise, and Xi, = min{Xi, Ki}. A kernel-type density estimate of f, the density function of F w.r.t. Lebesgue measure on the Borel o-field, based on the censored data (δi, Xi), i = 1,.,.,n, is considered. Weak and strong uniform consistency properties over the whole real line are studied. Rates of convergence results are established under higher-order differentiability assumption on f. A procedure for relaxing such assumptions is also proposed. 相似文献
3.
Andrzej Kozek 《Revue canadienne de statistique》1987,15(1):77-85
Let Xi, 1 ≤ i ≤ n, be independent identically distributed random variables with a common distribution function F, and let G be a smooth distribution function. We derive the limit distribution of □{ρα(Fn, G) - α(F, G)}, where Fn is the empirical distribution function based on X1,…,Xn and α is a Kolmogorov-Lévy-type metric between distribution functions. For α ≤ 0 and two distribution functions F and G the metric pα is given by pα(F, G) = inf {? ≤ 0: G(x - α?) - ? F(x) ≤ G(x + α?) + ? for all x ?}. 相似文献
4.
A basic concept for comparing spread among probability distributions is that of dispersive ordering. Let X and Y be two random variables with distribution functions F and G, respectively. Let F
−1 and G
−1 be their right continuous inverses (quantile functions). We say that Y is less dispersed than X (Y≤
disp
X) if G
−1(β)−G
−1(α)≤F
−1(β)−F
−1(α), for all 0<α≤β<1. This means that the difference between any two quantiles of G is smaller than the difference between the corresponding quantiles of F. A consequence of Y≤
disp
X is that |Y
1−Y
2| is stochastically smaller than |X
1−X
2| and this in turn implies var(Y)≤var(X) as well as E[|Y
1−Y
2|]≤E[|X
1−X
2|], where X
1, X
2 (Y
1, Y
2) are two independent copies of X(Y). In this review paper, we give several examples and applications of dispersive ordering in statistics. Examples include those
related to order statistics, spacings, convolution of non-identically distributed random variables and epoch times of non-homogeneous
Poisson processes.
This work was supported in part by KOSEF through Statistical Research Center for Complex Systems at Seoul National University.
Subhash Kochar is thankful to Dr. B. Khaledi for many helpful discussions. 相似文献
5.
《统计学通讯:理论与方法》2013,42(9):1767-1788
Abstract Let X 1, …, X m and Y 1, …, Y n be independent random variables, where X 1, …, X m are i.i.d. with continuous distribution function (df) F, and Y 1, …, Y n are i.i.d. with continuous df G. For testing the hypothesis H 0: F = G, we introduce and study analogues of the celebrated Kolmogorov–Smirnov and one- and two-sided Cramér-von Mises statistics that are functionals of a suitably integrated two-sample empirical process. Furthermore, we characterize those distributions for which the new tests are locally Bahadur optimal within the setting of shift alternatives. 相似文献
6.
7.
Irène Gijbels Marek Omelka Noël Veraverbeke 《Scandinavian Journal of Statistics》2015,42(4):1109-1126
This paper is concerned with studying the dependence structure between two random variables Y1 and Y2 in the presence of a covariate X, which affects both marginal distributions but not the dependence structure. This is reflected in the property that the conditional copula of Y1 and Y2 given X, does not depend on the value of X. This latter independence often appears as a simplifying assumption in pair‐copula constructions. We introduce a general estimator for the copula in this specific setting and establish its consistency. Moreover, we consider some special cases, such as parametric or nonparametric location‐scale models for the effect of the covariate X on the marginals of Y1 and Y2 and show that in these cases, weak convergence of the estimator, at ‐rate, holds. The theoretical results are illustrated by simulations and a real data example. 相似文献
8.
Saralees Nadarajah 《Statistics》2013,47(6):535-545
The distributions of linear combinations, products and ratios of random variables arise in many areas of engineering. In this paper, the exact distributions of the linear combination α X+β Y, the product |X Y| and the ratio |X/Y| are derived when X and Y are independent Laplace random variables. The Laplace distribution, being the oldest model for continuous data, has been one of the most popular models for measurement errors in engineering. 相似文献
9.
Let (X i , Y i ), i = 1, 2,…, n be independent and identically distributed random variables from some continuous bivariate distribution. If X (r) denotes the rth-order statistic, then the Y's associated with X (r) denoted by Y [r] is called the concomitant of the rth-order statistic. In this article, we derive an analytical expression of Shannon entropy for concomitants of order statistics in FGM family. Applying this expression for some well-known distributions of this family, we obtain the exact form of Shannon entropy, some of the information properties, and entropy bounds for concomitants of order statistics. Some comparisons are also made between the entropy of order statistics X (r) and the entropy of its concomitants Y [r]. In this family, we show that the mutual information between X (r) and Y [r], and Kullback–Leibler distance among the concomitants of order statistics are all distribution-free. Also, we compare the Pearson correlation coefficient between X (r) and Y [r] with the mutual information of (X (r), Y [r]) for the copula model of FGM family. 相似文献
10.
Serkan Eryilmaz 《统计学通讯:理论与方法》2017,46(24):12324-12335
This paper introduces a new class of bivariate lifetime distributions. Let {Xi}i ? 1 and {Yi}i ? 1 be two independent sequences of independent and identically distributed positive valued random variables. Define T1 = min?(X1, …, XM) and T2 = min?(Y1, …, YN), where (M, N) has a discrete bivariate phase-type distribution, independent of {Xi}i ? 1 and {Yi}i ? 1. The joint survival function of (T1, T2) is studied. 相似文献
11.
《Journal of Statistical Computation and Simulation》2012,82(10):1071-1082
The exact distributions of X+Y, X Y and X/(X+Y) are studied when X and Y are independent Pareto and gamma random variables. Applications are discussed, to real problems in clinical trials, computer networks and economics. 相似文献
12.
Let X1,X2,…,Xp be p random variables with cdf's F1(x),F2(x),…,Fp(x)respectively. Let U = min(X1,X2,…,Xp) and V = max(X1,X2,…,Xp).In this paper we study the problem of uniquely determining and estimating the marginal distributions F1,F2,…,Fp given the distribution of U or of V. First the problem of competing and complementary risks are introduced with examples and the corresponding identification problems are considered when the X1's are independently distributed and U(V) is identified, as well as the case when U(V) is not identified. The case when the X1's are dependent is considered next. Finally the problem of estimation is considered. 相似文献
13.
Let Xi≤?≤Xm and Yi≤?≤Yn be two sets of independent order statistics from continous distributions with distribution functions F and G respectively. Let Ri denote the rank of Xi in the combined order sample. Steck (1980) has found an expression for P(bi≤Ri≤ai, all i) when F = h(G), h being the incomplete beta function with parameters (α,β?α+1). An alternative expression for the same probability is obtained which is computationally a substantial improvement on Steck's result. 相似文献
14.
In this paper, by assuming that (X, Y 1, Y 2)T has a trivariate elliptical distribution, we derive the exact joint distribution of X and a linear combination of order statistics from (Y 1, Y 2)T and show that it is a mixture of unified bivariate skew-elliptical distributions. We then derive the corresponding marginal and conditional distributions for the special case of t kernel. We also present these results for an exchangeable case with t kernel and illustrate the established results with an air-pollution data. 相似文献
15.
Janusz Wywiał 《Statistical Papers》2004,45(3):413-431
LetF(x,y) be a distribution function of a two dimensional random variable (X,Y). We assume that a distribution functionF
x(x) of the random variableX is known. The variableX will be called an auxiliary variable. Our purpose is estimation of the expected valuem=E(Y) on the basis of two-dimensional simple sample denoted by:U=[(X
1, Y1)…(Xn, Yn)]=[X Y]. LetX=[X
1…X
n]andY=[Y
1…Y
n].This sample is drawn from a distribution determined by the functionF(x,y). LetX
(k)be the k-th (k=1, …,n) order statistic determined on the basis of the sampleX. The sampleU is truncated by means of this order statistic into two sub-samples:
% MathType!End!2!1! and
% MathType!End!2!1!.Let
% MathType!End!2!1! and
% MathType!End!2!1! be the sample means from the sub-samplesU
k,1 andU
k,2, respectively. The linear combination
% MathType!End!2!1! of these means is the conditional estimator of the expected valuem. The coefficients of this linear combination depend on the distribution function of auxiliary variable in the pointx
(k).We can show that this statistic is conditionally as well as unconditionally unbiased estimator of the averagem. The variance of this estimator is derived.
The variance of the statistic
% MathType!End!2!1! is compared with the variance of the order sample mean. The generalization of the conditional estimation
of the mean is considered, too. 相似文献
16.
Serkan Eryilmaz 《统计学通讯:理论与方法》2013,42(9-10):1925-1933
ABSTRACT Concomitants of order statistics are considered for the situation in which the random vectors (X 1, Y 1), (X 2, Y 2),…, (X n , Y n ) are independent but otherwise arbitrarily distributed. The joint and marginal distributions of the concomitants of order statistics and stochastic comparisons among the concomitants of order statistics are studied in this situation. 相似文献
17.
Nancy Lo Ferguson 《Australian & New Zealand Journal of Statistics》1973,15(3):191-209
Given a random sample(X1, Y1), …,(Xn, Yn) from a bivariate (BV) absolutely continuous c.d.f. H (x, y), we consider rank tests for the null hypothesis of interchangeability H0: H(x, y). Three linear rank test statistics, Wilcoxon (WN), sum of squared ranks (SSRN) and Savage (SN), are described in Section 1. In Section 2, asymptotic relative efficiency (ARE) comparisons of the three types of tests are made for Morgenstern (Plackett, 1965) and Moran (1969)BV alternatives with marginal distributions satisfying G(x) = F(x/θ) for some θ≠ 1. Both gamma and lognormal marginal distributions are used. 相似文献
18.
Di Chen Jye‐Chyi Lu Chin‐Shang Li Jinho Park 《Australian & New Zealand Journal of Statistics》2000,42(3):323-336
When two‐component parallel systems are tested, the data consist of Type‐II censored data X(i), i= 1, n, from one component, and their concomitants Y [i] randomly censored at X(r), the stopping time of the experiment. Marshall & Olkin's (1967) bivariate exponential distribution is used to illustrate statistical inference procedures developed for this data type. Although this data type is motivated practically, the likelihood is complicated, and maximum likelihood estimation is difficult, especially in the case where the parameter space is a non‐open set. An iterative algorithm is proposed for finding maximum likelihood estimates. This article derives several properties of the maximum likelihood estimator (MLE) including existence, uniqueness, strong consistency and asymptotic distribution. It also develops an alternative estimation method with closed‐form expressions based on marginal distributions, and derives its asymptotic properties. Compared with variances of the MLEs in the finite and large sample situations, the alternative estimator performs very well, especially when the correlation between X and Y is small. 相似文献
19.
The authors establish the joint distribution of the sum X and the maximum Y of IID exponential random variables. They derive exact formuli describing the random vector (X, Y), including its joint PDF, CDF, and other characteristics; marginal and conditional distributions; moments and related parameters; and stochastic representations leading to further properties of infinite divisibility and self-decomposability. The authors also discuss parameter estimation and include an example from climatology that illustrates the modeling potential of this new bivariate model. 相似文献
20.
Given two jointly observed random vectors Y and Z of the same dimension, let Y be a reordered version of Y and Z the resulting vector of concomitants of order statistics. When X is a covariate of interest, also jointly observed with Y, the authors obtain the joint covariance structure of (X, y, Z) and the related correlation parameters explicitly, under the assumption that the vector (X, Y, Z) is normal and that its joint covariance structure is permutation symmetric. They also discuss extensions to elliptically contoured distributions. 相似文献