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21.
Data that are proportions arise frequently in all areas of the sciences and engineering. In this
paper, the exact distributions of R=X+Y and W=X/(X+Y) and the corresponding moment properties are derived
when X and Y are proportions and arise from the most flexible bivariate beta distribution known to date.
The associated estimation procedures are developed. Finally, an application is illustrated to compositional
data of lavas from Skye. 相似文献
22.
23.
If X and Y are gamma distributed independent random variables then it is well known that the ratio X / (X + Y) has the beta distribution. In this note, the distribution of W = X / (X + Y) is considered when X and Y have the compound gamma distribution. We refer to the distribution of W as compound beta and describe an application to consumer price indices to show that compound beta is a better model than one based on the
standard beta distribution. We derive various properties of W, including its probability density function, cumulative distribution function, hazard rate function and moments. 相似文献
24.
A new three-parameter distribution with decreasing, increasing, and bathtub-shaped hazard rates obtained by compounding geometric, power series, and exponential distributions is introduced. It includes some well-known distributions as particular cases. Various mathematical properties of the new distribution as well as details of the maximum likelihood estimation and a sensitivity analysis for its parameters are presented. Finally, two real data applications are presented. 相似文献
25.
Mojtaba Alizadeh Seyyed Fazel Bagheri Mohammad Alizadeh Saralees Nadarajah 《Journal of applied statistics》2017,44(5):767-797
Generalizing lifetime distributions is always precious for applied statisticians. In this paper, we introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley geometric (EPLG) distribution, obtained by compounding EPL and geometric distributions. The new distribution arises in a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The distribution exhibits decreasing, increasing, unimodal and bathtub-shaped hazard rate functions, depending on its parameters. It contains several lifetime distributions as particular cases: EPL, new generalized Lindley, generalized Lindley, power Lindley and Lindley geometric distributions. We derive several properties of the new distribution such as closed-form expressions for the density, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Simulation studies are also provided. Finally, two real data applications are given for showing the flexibility and potentiality of the new distribution. 相似文献
26.
Given a sample from a normal population unbiased estimators are obtained for positive powers of the mean and estimators of almost exponentially small bias are obtained for negative powers of the mean. Simulation studies show superior performance of these estimators versus known ones. 相似文献
27.
Saralees Nadarajah 《Statistics》2013,47(4):437-439
An explicit closed form is derived for the characteristic function for the skew generalized t distribution studied by Arslan and Genç [The skew generalized t (SGT) distribution as the scale mixture of a skew exponential power distribution and its applications in robust estimation, Statistics 43(5) (2009), pp. 481–498]. The expression involves the Wright generalized hypergeometric Ψ–function. 相似文献
28.
Summary: The distributions of the product XY and the ratio X/Y are derived when X and Y are gamma and beta random variables distributed independently of each other. Tabulations of the associated percentage points
and illustrations of their practical use are also provided.
* The authors would like to thank the referee and the editor for carefully reading the paper and for their help in improving
the paper. 相似文献
29.
S. Nadarajah C. W. Anderson & J. A. Tawn 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1998,60(2):473-496
Multivariate extreme value models and associated statistical methods are developed for vector observations whose components are subject to an order restriction. The approach extends the multivariate threshold methodology of Coles and Tawn, Joe and co-workers and Smith and co-workers. The results are illustrated by an analysis of extreme rainfalls of different durations, and by a study of the problem of linking a long series of daily rainfall extremes with a partially overlapping shorter series of hourly extremes. 相似文献
30.
A new bivariate beta distribution capable of providing better fits than all its competitors is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure. Applications to six bivariate data sets are illustrated. 相似文献