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21.
In this paper, we consider characterizations of geometric distribution based on some properties of progressively Type-II right-censored order statistics. Specifically, we establish characterizations through conditional expectation, identical distribution, and independence of functions of progressively Type-II right-censored order statistics. Moreover, extensions of these results to generalized order statistics are also sketched. These generalize the corresponding results known for the case of ordinary order statistics. 相似文献
22.
23.
Let X
1, X
2,... be iid random variables (rv's) with the support on nonnegative integers and let (W
n
, n≥0) denote the corresponding sequence of weak record values. We obtain new characterization of geometric and some other discrete
distributions based on different forms of partial independence of rv's W
n
and W
n+r
—W
n
for some fixed n≥0 and r≥1. We also prove that rv's W
0 and W
n+1
—W
n
have identical distribution if and only if (iff) the underlying distribution is geometric. 相似文献
24.
25.
Synthetic and composite estimation under a superpopulation model 总被引:1,自引:1,他引:0
Under a simple superpopulation model for an arbitrary sampling design we derive optimal linear unbiased estimators/predictors
of a mean in a domain. They can be viewed as synthetic and composite estimators of small area estimation theory when no auxiliary
variable is available. Moreover, we show that the only requirement for optimality of a sampling strategy is to use any sampling
plan of fixed sample size together with traditional estimators (as designed for simple random sampling without replacement).
Finally, for symmetric sampling plans, simplified formulas (based on the first two moments of sample sizes) for optimal synthetic
and composite estimators and their MSE’s are derived. Throughout the paper we consistently use the model-design setup. 相似文献
26.
Ryszard Zieliński 《Statistics》2013,47(4):453-462
According to Pitman's Measure of Closeness, if T1and T2are two estimators of a real parameter $[d], then T1is better than T2if Po[d]{\T1-o[d] < \T2-0[d]\} > 1/2 for all 0[d]. It may however happen that while T1is better than T2and T2is better than T3, T3is better than T1. Given q ? (0,1) and a sample X1, X2, ..., Xnfrom an unknown F ? F, an estimator T* = T*(X1,X2...Xn)of the q-th quantile of the distribution F is constructed such that PF{\F(T*)-q\ <[d] \F(T)-q\} >[d] 1/2 for all F?F and for all T€T, where F is a nonparametric family of distributions and T is a class of estimators. It is shown that T* =Xj:n'for a suitably chosen jth order statistic. 相似文献
27.
The receiver operating characteristic (ROC) curve is a graphical representation of the relationship between false positive and true positive rates. It is a widely used statistical tool for describing the accuracy of a diagnostic test. In this paper we propose a new nonparametric ROC curve estimator based on the smoothed empirical distribution functions. We prove its strong consistency and perform a simulation study to compare it with some other popular nonparametric estimators of the ROC curve. We also apply the proposed method to a real data set. 相似文献
28.
29.
Dariusz Uciski Barbara Bogacka 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2005,67(1):3-18
Summary. The paper is concerned with a problem of finding an optimum experimental design for discriminating between two rival multiresponse models. The criterion of optimality that we use is based on the sum of squares of deviations between the models and picks up the design points for which the divergence is maximum. An important part of our criterion is an additional vector of experimental conditions, which may affect the design. We give the necessary conditions for the design and the additional parameters of the experiment to be optimum, we present the algorithm for the numerical optimization procedure and we show the relevance of these methods to dynamic systems, especially to chemical kinetic models. 相似文献
30.
A function \(f:V(G)\rightarrow \mathcal P (\{1,\ldots ,k\})\) is called a \(k\) -rainbow dominating function of \(G\) (for short \(kRDF\) of \(G)\) if \( \bigcup \nolimits _{u\in N(v)}f(u)=\{1,\ldots ,k\},\) for each vertex \( v\in V(G)\) with \(f(v)=\varnothing .\) By \(w(f)\) we mean \(\sum _{v\in V(G)}\left|f(v)\right|\) and we call it the weight of \(f\) in \(G.\) The minimum weight of a \( kRDF\) of \(G\) is called the \(k\) -rainbow domination number of \(G\) and it is denoted by \(\gamma _{rk}(G).\) We investigate the \(2\) -rainbow domination number of Cartesian products of cycles. We give the exact value of the \(2\) -rainbow domination number of \(C_{n}\square C_{3}\) and we give the estimation of this number with respect to \(C_{n}\square C_{5},\) \((n\ge 3).\) Additionally, for \(n=3,4,5,6,\) we show that \(\gamma _{r2}(C_{n}\square C_{5})=2n.\) 相似文献