Stochastic properties of spacings based on order statistics
نویسندگان
چکیده
Motivated in part by applications in reliability theory, life testing, and other areas, like finance or engineering, several authors have investigated the stochastic properties of order statistics and their spacings in the case when the observations are independent and identically distributed (i.i.d.). However, in some real situations, observations are non-i.i.d. Due to the complicated expression of the distribution in the non-i.i.d. case, only limited results are found in the literature. In this article, we present stochastic properties involving spacings between order statistics from underlying heterogeneous distributions.
منابع مشابه
On Multivariate Likelihood Ratio Ordering among Generalized Order Statistics and their Spacings
The most of the results obtained about stochastic properties of generalized order statistics and their spacings in the literature are based on equal model parameters. In this paper, with less restrictive conditions on the model parameters, we prove some new multivariate likelihood ratio ordering results between two sub-vectors of GOS's as well as two sub-vectors of $p$-spacings based on two con...
متن کاملOrdering Conditional Distributions of Spacings of Generalized Order Statistics
The purpose of this paper is to investigate conditions on the underlying distribution functions and the parameters, on which the generalized order statistics are based on, to establish the usual stochastic and the likelihood ratio orderings of general p-spacings by conditioning on the right tail of another lower indexed generalized order statistics. Some potential applications are also given.
متن کاملAsymptotic Distributions of Estimators of Eigenvalues and Eigenfunctions in Functional Data
Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...
متن کاملMultivariate Spacings Based on Data Depth : I . Construction of Nonparametric Multivariate Tolerance Regions
This paper introduces and studies multivariate spacings. The spacings are developed using the order statistics derived from data depth. Specifically, the spacing between two consecutive order statistics is the region which bridges the two order statistics, in the sense that the region contains all the points whose depth values fall between the depth values of the two consecutive order statistic...
متن کاملStochastic Orderings among Order Statistics and Sample Spacings
In this paper we review some of the results obtained recently in the area of stochastic comparisons of order statistics and sample spacings. We consider the cases when the parent observations are identically as well as non-identically distributed. But most of the time we shall be assuming that the observations are independent. The case of independent exponentials with unequal scale parameters i...
متن کامل