1,721,952 research outputs found
Multivariate Measures of Skewness for the Skew-Normal distribution
No full textThe main objective of this work is to calculate and compare different measures of
multivariate skewness for the skew-normal family of distributions. For this purpose,
we consider the Mardia (1970), Malkovich and Afifi (1973), Isogai (1982),
Srivastava (1984), Song (2001), Móri et al. (1993), Balakrishnan et al. (2007) and Kollo (2008) measures of skewness. The exact expressions of all measures of
skewness, except for Song’s, are derived for the family of skew-normal distributions, while
Song’s measure of shape is approximated by the use of delta method. The behavior of these
measures, their similarities and differences, possible interpretations, and their practical use
in testing for multivariate normal are studied by evaluating their power in the case of some
specific members of the multivariate skew-normal family of distributions
On weighted extropies
Full text linkThe extropy is a measure of information introduced as dual to entropy. It is a shift-independent information measure just as the entropy. We introduce here the notion of weighted extropy, a shift-dependent information measure which gives higher weights to larger values of random variables. We also study the weighted residual and past extropies as weighted versions of extropy for residual and past lifetimes. Bivariate versions extropy and weighted extropy are also described. Several examples are presented through out to illustrate all the concepts introduced here
A unified formulation of entropy and its application
Full text linkIn this paper, a general formulation of entropy is proposed. It depends on two parameters and includes Shannon, Tsallis and fractional entropy, all as special cases. This measure of information is referred to as fractional Tsallis entropy and some of its properties are then studied. Furthermore, the corresponding entropy in the context of Dempster–Shafer theory of evidence is proposed and referred to as fractional version of Tsallis–Deng entropy. Finally, an application to two classification problems is presented
On Tsallis extropy with an application to pattern recognition
Full text linkRecently, a new measure of information called extropy has been introduced by Lad, Sanfilippo and Agrò as the dual version of Shannon entropy. In the literature, Tsallis introduced a measure for a discrete random variable, named Tsallis entropy, as a generalization of Boltzmann–Gibbs statistics. In this work, a new measure of discrimination, called Tsallis extropy, is introduced and some of its properties are then discussed. The relation between Tsallis extropy and entropy is given and some bounds are also presented. Finally, an application of this extropy to pattern recognition is demonstrated
On Cumulative Entropies in Terms of Moments of Order Statistics
Full text linkIn this paper, relations between some kinds of cumulative entropies and moments of order statistics are established. By using some characterizations and the symmetry of a non-negative and absolutely continuous random variable X, lower and upper bounds for entropies are obtained and illustrative examples are given. By the relations with the moments of order statistics, a method is shown to compute an estimate of cumulative entropies and an application to testing whether data are exponentially distributed is outlined
Optimal Design for Accelerated-Stress Acceptance Test Based on Wiener Process
Full text linkTsai, C. C.*, Balakrishnan, N., and Lin, C. T. (2015), “Optimal Design for Accelerated-Stress Acceptance Test Based on Wiener Process,”智慧科技與應用統計研討會, Department of Statistics, Tamkang University, May 30. [MOST 103-2118-M-032-002-]補正完
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Confidence intervals for quantiles of a two-parameter exponential distribution with progressive censoring
No full textDispersion indices based on Kerridge inaccuracy measure and Kullback-Leibler divergence
Full text linkRecently, a new dispersion index, as a measures of information, has been introduced and called varentropy. In this article, we introduce new measures of variability based on two measures of uncertainty, namely, the Kerridge inaccuracy measure and the Kullback-Leibler divergence. Their generating functions are considered and their infinite series representations are given. These new measures and associated properties, bounds and illustrative examples are all presented in detail. Finally, an application of Kullback-Leibler divergence and its dispersion index is illustrated by using the mean-variance rule
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