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Abstract. In this work, for an exchangeable sequence of random variables {Xi, i1}, and two nondecreasing sequences of positive integers {hn, n2} and {kn, n2}, where hn+knn, n2, we prove that {Rn,hn,kn/n, n2} forms a reverse submartingale sequence, where , and X1,nX2,nXn,n are the order statistics based on {X1,,Xn}.
Abstract. In this paper, we develop procedures for obtaining confidence intervals for the parameters of a Laplace distribution as well as upper and lower probability tolerance intervals for a proportion , given a progressively Type-II right censored sample from the Laplace distribution. The intervals are obtained by conditioning on the observed values of the ancillary statistics. The intervals are...
Sharp lower and upper bounds on expected values of generalized order statistics are proven by the use of Morigutis inequality combined with the Young inequality. The bounds are expressed in terms of exponential moments or entropy. They are attainable providing new characterizations of some nontrivial distributions.
By combining the Moriguti and Steffensen inequalities, we obtain sharp upper bounds for the expectations of arbitrary linear combinations of order statistics from iid samples. The bounds are expressed in terms of expectations of the left truncated parent distribution and constants that depend only on the coefficients of the linear combination. We also present analogous results for dependent id samples...
In this work we propose a technique of estimating the location parameter μ and scale parameter σ of log-gamma distribution by U-statistics constructed by taking best linear functions of order statistics as kernels. The efficiency comparison of the proposed estimators with respect to maximum likelihood estimators is also made.
We study properties of the mean residual life functions of finite mixtures. Specifically, we study ordering properties, monotonicity and the limiting behaviour. We show, under some mild conditions, that the limiting behaviour is similar to that of the strongest member (in the mean residual life order) of the mixture. We also consider the case of negative mixtures (i.e., mixtures with some negative...
Let $$X_{1},\ldots,X_{n}$$ be independent and identically distributed random variables with continuous distribution function. Denote by $$X_{1:n} \leq \cdots \leq X_{n:n}$$ the corresponding order statistics. In the present paper, the concept of $$\varepsilon$$ -neighbourhood runs, which is an extension of the usual run concept to the continuous case, is developed for the sequence of...
Let X1, X2, ..., Xn be independent exponential random variables such that Xi has failure rate λ for i = 1, ..., p and Xj has failure rate λ* for j = p + 1, ..., n, where p ≥ 1 and q = n − p ≥ 1. Denote by Di:n (p,q) = Xi:n−Xi-1:n the ith spacing of the order statistics X1:n≤ X2:n ≤ ... ≤ Xn:n, i = 1, ..., n, where X0:n ≡ 0. The purpose of this paper is to investigate multivariate...
A reliability experimenter is often interested in studying the effects of extreme or varying stress factors such as load, pressure, temperature and voltage on the lifetimes of experimental units. Accelerated life-tests allow the experimenter to vary the levels of these stress factors in order to obtain information on the parameters of the lifetime distributions more rapidly than under normal operating...
Classical control charts are very sensitive to deviations from normality. In this respect, nonparametric charts form an attractive alternative. However, these often require considerably more Phase I observations than are available in practice. This latter problem can be solved by introducing grouping during Phase II. Then each group minimum is compared to a suitable upper limit (in the two-sided case...
This paper is devoted to the analysis of the estimation of the mean of a sensitive variable. The use of a randomized response (RR) procedure gives confidence to the interviewed that his privacy is protected. We consider that a simple random sampling with replacement design is used for selecting a sample. The behavior of the RR procedure, when ranked set sampling is the design used, is developed under...
It is shown that if (X1, X2, . . . , Xn) is a random vector with a logconcave (logconvex) joint reliability function, then XP = mini∈PXi has increasing (decreasing) hazard rate. Analogously, it is shown that if (X1, X2, . . . , Xn) has a logconcave (logconvex) joint distribution function, then XP = maxi∈PXi has decreasing (increasing) reversed hazard rate. If the random...
In the present paper, we consider a (n − k + 1)-out-of-n system with identical components where it is assumed that the lifetimes of the components are independent and have a common distribution function F. We assume that the system fails at time t or sometime before t, t > 0. Under these conditions, we are interested in the study of the mean time elapsed since the failure of the components. We...
Some results on the relationships between distributions of order statistics and of spacings are presented. These results are then used to establish a characterization of the uniform distribution extending some existing results in this direction.
Let X1, . . . , Xn be independent exponential random variables with respective hazard rates λ1, . . . , λn, and Y1, . . . , Yn be independent and identically distributed random variables from an exponential distribution with hazard rate λ. Then, we prove that X2:n, the second order statistic from X1, . . . , Xn, is larger than Y2:n, the second order statistic from Y1, . . . , Y...
In this paper, we discuss the statistical inference of the lifetime distribution of components based on observing the system lifetimes when the system structure is known. A general proportional hazard rate model for the lifetime of the components is considered, which includes some commonly used lifetime distributions. Different estimation methods—method of moments, maximum likelihood method and least...
We consider a (n − k + 1)-out-of-n system with independent and nonidentical components. Under the condition that at time t the system has failed we study the past lifetime of the components of the system. The mean past lifetime of the components is defined and some of its properties are investigated. Stochastic comparisons are also made between the past lifetime of different systems.
In the two-sample prediction problem, record values from the present sample may be used as predictors of order statistics from a future sample. In this paper, we investigate the nearness of record statistics (upper and lower) to order statistics from a location-scale family of distributions in the sense of Pitman closeness and discuss the corresponding monotonicity properties. We then determine the...
Given a large sample from a location-scale population we estimate the unknown parameters by means of confidence regions constructed on the basis of two order statistics. The problem of the best choice of those statistics to obtain good estimates, as $$n\rightarrow \infty ,$$ is considered.
In this note, we consider a coherent system with the property that, upon failure of the system, some of its components remain unfailed in the system. Under this condition, we study the residual lifetime of the live components of the system. Signature based mixture representation of the joint and marginal reliability functions of the live components are obtained. Various stochastic and aging properties...
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