共查询到20条相似文献,搜索用时 15 毫秒
1.
P.J. Huber 《Statistics》2013,47(1):41-53
Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon's entropy (see Rao et al. [Cumulative residual entropy: A new measure of information, IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding, in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi's entropy, and study its properties. We also examine it in relation to some applied problems such as weighted and equilibrium models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing relationships to identify different bivariate lifetime models. 相似文献
2.
Jorge Navarro Yolanda del Aguila Majid Asadi 《Journal of statistical planning and inference》2010,140(1):1931
The residual entropy function is a relevant dynamic measure of uncertainty in reliability and survival studies. Recently, Rao et al. [2004. Cumulative residual entropy: a new measure of information. IEEE Transactions on Information Theory 50, 1220–1228] and Asadi and Zohrevand [2007. On the dynamic cumulative residual entropy. Journal of Statistical Planning and Inference 137, 1931–1941] define the cumulative residual entropy and the dynamic cumulative residual entropy, respectively, as some new measures of uncertainty. They study some properties and applications of these measures showing how the cumulative residual entropy and the dynamic cumulative residual entropy are connected with the mean residual life function. In this paper, we obtain some new results on these functions. We also define and study the dynamic cumulative past entropy function. Some results are given connecting these measures of a lifetime distribution and that of the associated weighted distribution. 相似文献
3.
4.
Antonio Di Crescenzo Maria Longobardi 《Journal of statistical planning and inference》2009,139(12):4072-4087
In analogy with the cumulative residual entropy recently proposed by Wang et al. [2003a. A new and robust information theoretic measure and its application to image alignment. In: Information Processing in Medical Imaging. Lecture Notes in Computer Science, vol. 2732, Springer, Heidelberg, pp. 388–400; 2003b. Cumulative residual entropy, a new measure of information and its application to image alignment. In: Proceedings on the Ninth IEEE International Conference on Computer Vision (ICCV’03), vol. 1, IEEE Computer Society Press, Silver Spring, MD, pp. 548–553], we introduce and study the cumulative entropy, which is a new measure of information alternative to the classical differential entropy. We show that the cumulative entropy of a random lifetime X can be expressed as the expectation of its mean inactivity time evaluated at X. Hence, our measure is particularly suitable to describe the information in problems related to ageing properties of reliability theory based on the past and on the inactivity times. Our results include various bounds to the cumulative entropy, its connection to the proportional reversed hazards model, and the study of its dynamic version that is shown to be increasing if the mean inactivity time is increasing. The empirical cumulative entropy is finally proposed to estimate the new information measure. 相似文献
5.
Saeid Tahmasebi 《统计学通讯:理论与方法》2020,49(21):5196-5219
AbstractIn this paper, we consider weighted extensions of generalized cumulative residual entropy and its dynamic(residual) version. Our results include linear transformations, stochastic ordering, bounds, aging class properties and some relationships with other reliability concepts. We also define the conditional weighted generalized cumulative residual entropy and discuss some properties of its. For these concepts, we obtain some characterization results under some assumptions. Finally, we provide an estimator of the new information measure using empirical approach. In addition, we study large sample properties of this estimator. 相似文献
6.
M. Mirali 《统计学通讯:理论与方法》2017,46(22):11047-11059
Some extensions of Shannon entropy to the survival function have been recently proposed. Misagh et al. (2011) introduced weighted cumulative residual entropy (WCRE) that was studied more by Mirali et al. (2015). In this article, the dynamic version of WCRE is proposed. Some relationships of this measure with well-known reliability measures and ageing classes are studied and some characterization results for exponential and Rayleigh distributions are provided. Also, a non parametric estimation of dynamic version of WCRE is introduced and its asymptotic behavior is investigated. 相似文献
7.
Amit Ghosh 《统计学通讯:理论与方法》2020,49(6):1402-1421
AbstractRecently, the notion of cumulative residual Rényi’s entropy has been proposed in the literature as a measure of information that parallels Rényi’s entropy. Motivated by this, here we introduce a generalized measure of it, namely cumulative residual inaccuracy of order α. We study the proposed measure for conditionally specified models of two components having possibly different ages called generalized conditional cumulative residual inaccuracy measure. Several properties of generalized conditional cumulative residual inaccuracy measure including the effect of monotone transformation are investigated. Further, we provide some bounds on using the usual stochastic order and characterize some bivariate distributions using the concept of conditional proportional hazard rate model. 相似文献
8.
On the dynamic cumulative residual entropy 总被引:1,自引:0,他引:1
Recently, Rao et al. [(2004) Cumulative residual entropy: a new measure of information. IEEE Trans. Inform. Theory 50(6), 1220–1228] have proposed a new measure of uncertainty, called cumulative residual entropy (CRE), in a distribution function F and obtained some properties and applications of that. In the present paper, we propose a dynamic form of CRE and obtain some of its properties. We show how CRE (and its dynamic version) is connected with well-known reliability measures such as the mean residual life time. 相似文献
9.
Saralees Nadarajah 《AStA Advances in Statistical Analysis》2009,93(1):89-107
The probability distribution of the maximum of normalized SNRs (signal-to-noise ratios) is studied for wireless systems with
multiple branches. Explicit expressions and bounds are derived for the cumulative distribution function, probability density
function, hazard rate function, moment generating function, nth moment, variance, skewness, kurtosis, mean deviation, Shannon entropy, order statistics and the asymptotic distribution
of the extreme order statistics. Estimation procedures are derived by the methods of moments and maximum likelihood. An application
is illustrated with respect to performance assessment of wireless systems. 相似文献
10.
S. Minimol 《统计学通讯:理论与方法》2017,46(6):2816-2822
Recently, the concept of dynamic cumulative residual entropy and its generalizations has gained much attention among researchers. In this work, a new generalized dynamic cumulative measure in the past lifetime is proposed. Further, some characterization results connecting this new generalized dynamic entropy measure and other reversed measures are obtained. 相似文献
11.
Sangun Park 《Journal of Statistical Computation and Simulation》2017,87(3):563-576
In this paper, we suggest an extension of the cumulative residual entropy (CRE) and call it generalized cumulative entropy. The proposed entropy not only retains attributes of the existing uncertainty measures but also possesses the absolute homogeneous property with unbounded support, which the CRE does not have. We demonstrate its mathematical properties including the entropy of order statistics and the principle of maximum general cumulative entropy. We also introduce the cumulative ratio information as a measure of discrepancy between two distributions and examine its application to a goodness-of-fit test of the logistic distribution. Simulation study shows that the test statistics based on the cumulative ratio information have comparable statistical power with competing test statistics. 相似文献
12.
Saralees Nadarajah 《AStA Advances in Statistical Analysis》2011,95(3):219-251
The exponentiated exponential distribution, a most attractive generalization of the exponential distribution, introduced by
Gupta and Kundu (Aust. N. Z. J. Stat. 41:173–188, 1999) has received widespread attention. It appears, however, that many mathematical properties of this distribution have not
been known or have not been known in simpler/general forms. In this paper, we provide a comprehensive survey of the mathematical
properties. We derive expressions for the moment generating function, characteristic function, cumulant generating function,
the nth moment, the first four moments, variance, skewness, kurtosis, the nth conditional moment, the first four cumulants, mean deviation about the mean, mean deviation about the median, Bonferroni
curve, Lorenz curve, Bonferroni concentration index, Gini concentration index, Rényi entropy, Shannon entropy, cumulative
residual entropy, Song’s measure, moments of order statistics, L moments, asymptotic distribution of the extreme order statistics, reliability, distribution of the sum of exponentiated exponential
random variables, distribution of the product of exponentiated exponential random variables and the distribution of the ratio
of exponentiated exponential random variables. We also discuss estimation by the method of maximum likelihood, including the
case of censoring, and provide simpler expressions for the Fisher information matrix than those given by Gupta and Kundu.
It is expected that this paper could serve as a source of reference for the exponentiated exponential distribution and encourage
further research. 相似文献
13.
In this paper , we consider a measure of inaccuracy between distributions of the nth record value and parent random variable. We also propose the measure of residual inaccuracy of record values and study characterization results of dynamic cumulative residual inaccuracy measure. We discuss some properties of the proposed measures. 相似文献
14.
Vikas Kumar 《统计学通讯:理论与方法》2017,46(17):8343-8354
In this article, the concept of cumulative residual entropy (CRE) given by Rao et al. (2004) is extended to Tsallis entropy function and dynamic version, both residual and past of it. We study some properties and characterization results for these generalized measures. In addition, we provide some characterization results of the first-order statistic based on the Tsallis survival entropy. 相似文献
15.
A. Chamany 《统计学通讯:理论与方法》2014,43(6):1041-1049
In this article, we introduce a measure of discrepancy between two life-time distributions based on cumulative residual entropy. The dynamic form of this measure is considered and some of its properties are obtained. The relations between dynamic form and some well-known concepts in reliability such as mean residual life-time, hazard rate order, and new better (worse) than used are studied. 相似文献
16.
V. Zardasht 《Journal of Statistical Computation and Simulation》2019,89(8):1516-1525
In this paper, we introduce a new test for the dilation order based on cumulative residual Tsallis entropy of order α. The effect of the values of parameter α on the power of the test statistics is numerically investigated. The asymptotic distribution of the test statistic is given. The performance of the test statistic is evaluated using a simulation study. Finally, some numerical examples illustrating the theory are also given. 相似文献
17.
M. Ahsanullah 《Statistical Papers》1981,22(4):316-320
Let X be a non-negative random variable with cumulative probability distribution function F. Suppse X1, X2, ..., Xn be a random sample of size n from F and Xi,n is the i-th smallest order statistics. We define the standardized spacings Dr,n=(n-r) (Xr+1,n-Xr,n), 1≤r≤n, with DO,n=nX1,n and Dn,n=0. Characterizations of the exponential distribution are given by considering the expectation and hazard rates of Dr,n. 相似文献
18.
In analogy with the weighted Shannon entropy proposed by Belis and Guiasu (1968) and Guiasu (1986), we introduce a new information measure called weighted cumulative residual entropy (WCRE). This is based on the cumulative residual entropy (CRE), which is introduced by Rao et al. (2004). This new information measure is “length-biased” shift dependent that assigns larger weights to larger values of random variable. The properties of WCRE and a formula relating WCRE and weighted Shannon entropy are given. Related studies of reliability theory is covered. Our results include inequalities and various bounds to the WCRE. Conditional WCRE and some of its properties are discussed. The empirical WCRE is proposed to estimate this new information measure. Finally, strong consistency and central limit theorem are provided. 相似文献
19.
Recently, the concept of reversed mean residual life order based on the mean of the random variable X t = (t ? X | X ≤ t), t > 0, called the reversed residual life, defined for the nonnegative random variable X, has been introduced in the literature. In this paper, a stochastic order based on the shifted version of the reversed mean residual life is proposed, based on the reversed mean residual life function for a random variable X with support (l X , ∞), where l X may be negative infinity, and its properties are studied. Closure under the Poisson shock model and properties for spare allocation are also discussed. 相似文献
20.
《Journal of Statistical Computation and Simulation》2012,82(14):2823-2838
In some statistical applications, data may not be considered as a random sample of the whole population and some subjects have less probability of belonging to the sample. Consequently, statistical inferences for such data sets, usually yields biased estimation. In such situations, the length-biased version of the original random variable as a special weighted distribution often produces better inferences. An alternative weighted distribution based on the mean residual life is suggested to treat the biasedness. The Rayleigh distribution is applied in many real applications, hence the proposed method of weighting is performed to produce a new lifetime distribution based on the Rayleigh model. In addition, statistical properties of the proposed distribution is investigated. A simulation study and a real data set are prepared to illustrate that the mean residual weighted Rayleigh distribution gives a better fit than the original and also the length-biased Rayleigh distribution. 相似文献