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1.
Bayesian prediction of order statistics as well as the mean of a future sample based on observed record values from an exponential distribution are discussed. Several Bayesian prediction intervals and point predictors are derived. Finally, some numerical computations are presented for illustrating all the proposed inferential procedures. 相似文献
2.
M. M. Mohie El-Din 《统计学通讯:模拟与计算》2013,42(9):2703-2723
ABSTRACTBased on the observed dual generalized order statistics drawn from an arbitrary unknown distribution, nonparametric two-sided prediction intervals as well as prediction upper and lower bounds for an ordinary and a dual generalized order statistic from another iid sequence with the same distribution are developed. The prediction intervals for dual generalized order statistics based on the observed ordinary generalized order statistics are also developed. The coverage probabilities of these prediction intervals are exact and free of the parent distribution, F. Finally, numerical computations and real examples of the coverage probabilities are presented for choosing the appropriate limits of the prediction. 相似文献
3.
Some new identities among the m oments of order statistics are derived. These are more general in nature and are applicable when moments of Some extreme order statistics do not exist. 相似文献
4.
A simplified proof of the basic properties of the estimators in the Exponential Order Statistics (Jelinski-Moranda) Model is given. The method of constructing confidence intervals from hypothesis tests is applied to find conservative confidence intervals for the unknown parameters in the model. 相似文献
5.
We consider a five-dimensional normal distribution and derive the exact joint distribution one variable, linear combinations of order statistics from two other variables, and linear combinations of the corresponding concomitants of these order statistics. We show that this joint distribution is a mixture of trivariate unified skew-normal distributions. This mixture representation enables us to predict one variable based on linear combinations of order statistics from two other variables and linear combinations of the corresponding concomitants. We finally illustrate the usefulness of these results by using a real data. 相似文献
6.
《Journal of Statistical Computation and Simulation》2012,82(3):683-695
Prediction of censored order statistics from a Type-II censored sample can be done with trivial bounds having perfect confidence. However, given independent samples from the same absolutely continuous distribution, improved bounds can be attained. In this regard, we develop here point prediction based on L-statistics for predicting order statistics (OS) from a future sample as well as for predicting censored OS from a Type-II censored sample. An example is taken to illustrate these ideas, and the limiting case wherein a single independent sample is arbitrarily large is also discussed. 相似文献
7.
Vic Barnett 《统计学通讯:理论与方法》2013,42(7):2109-2118
Outliers are to be found among the extremes of a data set. Extremes are examples of order statistics. It is thus relevant to ask to what extent the statistical methods (and probabilistic properties) of outliers and of order statistics coincide and depend on each other. Whilst clear overlap is identifiable, aims and procedures are often quite distinct and each topic plays its own important role in the panoply of statistical principles and methodology. 相似文献
8.
《Journal of Statistical Computation and Simulation》2012,82(9):1725-1741
The problem of predicting future generalized-order statistics, by assuming the future sample size is a random variable, is discussed. A general expression for the coverage probability of the prediction intervals is derived. Since k-records and progressively type-II censored-order statistics are contained in the model of generalized-order statistics, the corresponding results for them can be deduced as special cases. When the future sample size has degenerate, binomial, Poisson and geometric distributions, numerical computations are given. The procedure for finding an optimal prediction interval is presented for each case. Finally, we apply our results to a real data set in life testing given in Lee and Wang [Statistical methods for survival data analysis. Hoboken, NJ: John Wiley and Sons; 2003, p. 58, Table 3.4] for illustrative the proposed procedure in this paper. 相似文献
9.
The standard approach to construct nonparametric tolerance intervals is to use the appropriate order statistics, provided a minimum sample size requirement is met. However, it is well-known that this traditional approach is conservative with respect to the nominal level. One way to improve the coverage probabilities is to use interpolation. However, the extension to the case of two-sided tolerance intervals, as well as for the case when the minimum sample size requirement is not met, have not been studied. In this paper, an approach using linear interpolation is proposed for improving coverage probabilities for the two-sided setting. In the case when the minimum sample size requirement is not met, coverage probabilities are shown to improve by using linear extrapolation. A discussion about the effect on coverage probabilities and expected lengths when transforming the data is also presented. The applicability of this approach is demonstrated using three real data sets. 相似文献
10.
《Journal of Statistical Computation and Simulation》2012,82(7):1320-1333
In reliability theory, risk analysis, renewal processes and actuarial studies, the residual lifetimes data play an important essential role in studying the conditional tail of the lifetime data. In this paper, based on some observed ordered residual Weibull data, we introduce different prediction methods for obtaining prediction intervals (PIs) of future residual lifetimes including likelihood, Wald, moments, parametric bootstrap, and highest conditional methods. Monte Carlo simulations are performed to compare the performances of the so obtained PIs and one data analysis is performed for illustration purposes. 相似文献
11.
M. M. Ali 《Revue canadienne de statistique》1976,4(1):151-153
A necessary and sufficient condition that two distributions having finite means are identical is that for any fixed integer r > 0, the expected values of their rth (n ? r) order statistics are equal [or the expected values of their (n-r)th (n > r ? 0) order statistics are equal] for all n where n is the sample size. 相似文献
12.
Philip Samuel 《Statistical Papers》2008,49(1):101-108
In this work, general forms of many well-known continuous probability distributions are characterized by conditional expectation of some functions of generalized order statistics. These results are the generalization of the characterization results based on conditional expectation of the functions of order statistics given by Khan and Abu-Salih (1989). 相似文献
13.
《Journal of Statistical Computation and Simulation》2012,82(3):526-544
In this paper, the problem of predicting the future sequential order statistics based on observed multiply Type-II censored samples of sequential order statistics from one- and two-parameter exponential distributions is addressed. Using the Bayesian approach, the predictive and survival functions are derived and then the point and interval predictions are obtained. Finally, two numerical examples are presented for illustration. 相似文献
14.
In a wide subclass of generalized order statistics, representations of marginal density and distribution functions are developed. The results are applied to obtain several relations, such as recurrence relations, and explicit expressions for the moments of generalized order statistics from Pareto, power function and Weibull distributions Moreover, characterizations of exponential distributions are shown by means of a distributional identity as well as by* an identity of expectations involving a subrange and a corresponding generalized order statistic. 相似文献
15.
Mahdi Teimouri 《统计学通讯:理论与方法》2013,42(11):3310-3322
ABSTRACTThe novel Balakrishnan skew-normal distribution introduced in 2008 has received considerable interest. Here, we derive stochastic representations for simulating order statistics of the novel Balakrishnan skew-normal distribution. The resulting algorithms are more efficient than the ordinary sorting algorithm. 相似文献
16.
koiti Takahasi 《统计学通讯:理论与方法》2013,42(12):4133-4136
Let Fk:m be the cumulative disribution function of the kth order statistic in a sample of size n from a distribution F(x) with density function f(x).The primary objective of this paper is to show that Fk+1mis IHR(increasing hazard rate) if Fkm(x)is IHH and that Fk-1:n(x)is DHR.(decreasing hazard rate) if Fkm(x) is DHR. 相似文献
17.
Agnieszka Goroncy 《统计学通讯:理论与方法》2017,46(24):11972-11987
We present the upper non positive bounds on the expectations of gOSs centered about the sample mean, which are based on the parent distributions with decreasing density and decreasing density on average distributions. Such bounds can be obtained only for particular cases of gOSs and they are expressed in units generated by the central absolute moments of a fixed order. The attainability conditions are also described. The method of deriving presented bounds is based on the maximization of appropriate norms over properly chosen convex sets. The paper complements the results of Bieniek [J. Statist. Plann. Inference, 2008; 138:971–981]. 相似文献
18.
In this paper, the two-parameter Pareto distribution is considered and the problem of prediction of order statistics from a future sample and that of its geometric mean are discussed. The Bayesian approach is applied to construct predictors based on observed k-record values for the cases when the future sample size is fixed and when it is random. Several Bayesian prediction intervals are derived. Finally, the results of a simulation study and a numerical example are presented for illustrating all the inferential procedures developed here. 相似文献
19.
Ray E. Schafer 《统计学通讯:模拟与计算》2013,42(5):643-644
20.
In this paper we give some properties of the expected values of any order statistic when one of its adjacent order statistics
is known (order mean function) from a sequence of sizen of independent and identically distributed random variables with discrete distribution. Furthermore, we obtain the explicit
expressions of the distribution from these order mean functions, and finally, we show the necessary and sufficient conditions
for any real function to be an order mean function. We also add some examples of characterization of discrete distributions
from the order mean functions.
Partially supported by Consejería de Cultura y Educación (C.A.R.M.), under Grant PIB 95/90. 相似文献