Rapid advances in modelling research have created new challenges and opportunities for statisticians. Statistical inference in observational studies and many other emerging fields have motivated ...statisticians worldwide to develop cutting-edge methods and analytical strategies. The aim of this reprint is to showcase the applications and methodological research in all fields of computational statistics. This reprint will provide a forum for computer scientists, mathematicians, and statisticians working in a variety of areas in statistics, including biometrics, econometrics, data analysis, graphics, and simulation.
The statistical characteristics of wind speed data recorded at nine buoys, located in Ionian and Aegean Sea (Eastern Mediterranean) are analyzed in this paper, in order to present a more accurate ...method for estimation of wind speed characteristics, according to the suitability of the probability distribution functions (pdf). This article has focussed on wind regimes that present nearly zero percentages of null wind speeds. The selected distributions for examination are the typical two-parameter Weibull wind speed distribution (W-pdf) and the two-component mixture Weibull distribution (WW-pdf), involving five parameters (two shape parameters, two scale parameters, and one proportionality parameter).
Suitable software, based on the maximum likelihood method, is used in order to estimate the aforementioned two-parameters of the typical W-pdf and the five parameters of the mixed WW-pdf. The suitability of the aforementioned distributions is judged from the coefficient of determination (
R
2) and the fit standard error (
RMSE) tests, which had been carried out between each one of the theoretical distributions and the corresponding experimental cumulative frequencies of the nine selected sites. From these tests it is clear that, in most cases (six experimental stations - having either unimodal or bimodal frequency distributions), mixed-Weibull distribution provides the highest degree of fit. In the other three cases, the mixing weight
p of the two-component mixed Weibull density function equals to zero (
p
=
0), so the mixed-Weibull distribution is been transformed to the typical Simple-Weibull distribution.
Hence, the general conclusion is that the aforementioned mixture of two Weibull distributions is more suitable for the description of such wind conditions and could offer less relative errors in determining the annual mean wind power density.
A fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is ...sufficiently general to encompass some recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew t-density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.
This book uses the EM (expectation maximization) algorithm to simultaneously estimate the missing data and unknown parameter(s) associated with a data set. The parameters describe the component ...distributions of the mixture; the distributions may be continuous or discrete.The editors provide a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions along with MCMC computational methods, together with a range of detailed discussions covering the applications of the methods and features chapters from the leading experts on the subject. The applications are drawn from scientific discipline, including biostatistics, computer science, ecology and finance. This area of statistics is important to a range of disciplines, and its methodology attracts interest from researchers in the fields in which it can be applied.
When a p×p$$ p\times p $$ real positive definite matrix S$$ S $$ follows a Wishart or, more generally, a matrix‐variate gamma distribution with shape parameter α$$ \alpha $$ and positive definite ...scale parameter matrix B$$ B $$, one can represent S$$ S $$ as XX′$$ X{X}^{\prime } $$ for some matrix X$$ X $$ of dimension p×q$$ p\times q $$. When p>q$$ p>q $$, S$$ S $$ has a singular distribution whose properties can be studied via the density function of X$$ X $$. It will be shown that when X$$ X $$ follows a matrix‐variate extended Gaussian distribution, the density function of the resulting singular gamma distribution can be obtained by making use of successive transformations and their associated Jacobians. The singular Wishart distribution will then be obtained as a particular case. The marginal and conditional density functions resulting from an arbitrary partitioning of X$$ X $$ will be considered as well. The same technique will also be applied to the derivation of the density functions of real and complex singular type‐1 and type‐2 beta‐distributed matrices. It so happens that the proposed approach, which is based on manipulations involving the wedge products of certain differential elements, generally proves more efficient than the intricate procedures that have hitherto been employed in the literature.
Résumé
Lorsqu'une matrice réelle définie positive S$$ S $$ (p×p)$$ \left(p\times p\right) $$ suit une loi de Wishart ou, plus généralement, une distribution gamma de paramètre de forme α$$ \alpha $$ et de paramètre d'échelle une matrice définie positive B$$ B $$, il est possible de représenter S$$ S $$ sous forme XX′$$ X{X}^{\prime } $$ où X$$ X $$ est une matrice de dimension p×q$$ p\times q $$. Lorsque p>q$$ p>q $$, S$$ S $$ a une distribution singulière dont les propriétés peuvent être étudiées via la fonction de densité de X$$ X $$. Les auteurs de cet article montrent que lorsque X$$ X $$ suit une distribution gaussienne étendue à variable matricielle, la fonction de densité de la distribution gamma singulière résultante peut être obtenue en utilisant des transformations successives et leurs Jacobiens associés. La distribution de Wishart singulière en découle comme un cas particulier. Le cas de fonctions de densité marginale et conditionnelle résultant d'un partitionnement arbitraire de X$$ X $$ a également été traité. La même technique a été utilisée pour déterminer les fonctions de densité de matrices singulières réelles et complexes de lois beta de type 1 et de type 2. Ainsi l'approche proposée, basée sur des manipulations mettant en jeu les produits extérieurs de certains éléments différentiels, s'avère généralement plus efficace que les procédures complexes utilisées jusqu'à présent dans la littérature.
In spite of widespread expectations of improvements in living standards and health conditions, in most of the countries of the former Soviet bloc the transition to the market economy was accompanied ...by a sharp increase in (already high) death rates. Such an increase provoked an 'excess mortality' of some three million people over the period 1989-96 alone, an unprecedented phenomenon in peacetime. Such a crisis remains poorly explained, has generated a limited policy response in the countries concerned and international organizations, and is bound to generate important political and economic repercussions. This book is the first comprehensive assessment of the mortality crisis in transitional economies, of its causes, and of its remedies on the basis - among others - of micro data sets and quasi-panels on health trends which have never been used before. Contributions by demographers, economists, sociologists, epidemiologists, and health experts provide a rigorous analysis of the upsurge in mortality rates, with the aim of contributing to the launch of vigorous policies to tackle the crisis. Available in OSO: http://www.oxfordscholarship.com/oso/public/content/economicsfinance/9780198297413/toc.html
One aim of data mining is the identification of interesting structures in data. For better analytical results, the basic properties of an empirical distribution, such as skewness and eventual ...clipping, i.e. hard limits in value ranges, need to be assessed. Of particular interest is the question of whether the data originate from one process or contain subsets related to different states of the data producing process. Data visualization tools should deliver a clear picture of the univariate probability density distribution (PDF) for each feature. Visualization tools for PDFs typically use kernel density estimates and include both the classical histogram, as well as the modern tools like ridgeline plots, bean plots and violin plots. If density estimation parameters remain in a default setting, conventional methods pose several problems when visualizing the PDF of uniform, multimodal, skewed distributions and distributions with clipped data, For that reason, a new visualization tool called the mirrored density plot (MD plot), which is specifically designed to discover interesting structures in continuous features, is proposed. The MD plot does not require adjusting any parameters of density estimation, which is what may make the use of this plot compelling particularly to non-experts. The visualization tools in question are evaluated against statistical tests with regard to typical challenges of explorative distribution analysis. The results of the evaluation are presented using bimodal Gaussian, skewed distributions and several features with already published PDFs. In an exploratory data analysis of 12 features describing quarterly financial statements, when statistical testing poses a great difficulty, only the MD plots can identify the structure of their PDFs. In sum, the MD plot outperforms the above mentioned methods.
In this study, a D-vine copulas modelling based probabilistic load flow (PLF) computation method is proposed, which considers the dependence among multiple wind generators. Furthermore, this method ...is not restricted by the type of wind speed distribution, i.e. allow random variables to comply with any types of distribution model. Copula theory plays an important role on dependency modelling. However, when high-dimensional correlation is taken into account, standard multivariate copula suffers from the problems of inflexible structure. Vine copula is flexible to build high-dimensional dependence and able to construct complicated dependence structure by applying bivariate copulas. For marginal distributions of wind speed, non-parametric model can provide a better estimation than those parametric models. An improved Latin hypercube sampling based Monte Carlo simulation method is utilised to solve PLF problems. A modified IEEE 33-node distribution system is used to conduct the numerical experiments for the accuracy and efficiency verification of the proposed PLF method, under the MatlabR2016a platform. The simulation results verify the outstanding accuracy, efficiency and robustness of the proposed PLF method.
In many applications, assumptions about the log-concavity of a probability distribution allow just enough special structure to yield a workable theory. This paper catalogs a series of theorems ...relating log-concavity and/or log-convexity of probability density functions, distribution functions, reliability functions, and their integrals. We list a large number of commonly-used probability distributions and report the log-concavity or log-convexity of their density functions and their integrals. We also discuss a variety of applications of log-concavity that have appeared in the literature.
While it is well known that the Weibull distribution is a good model for wind-speed measurements and can be explained through simple statistical arguments, how such a model holds for shorter time ...periods is still an open question. In this paper, we present a systematic investigation of the accuracy of the Weibull distribution to wind-speed measurements, in comparison with other possible “cousin” distributions. In particular, we show that the Gaussian distribution enables one to predict wind-speed histograms with higher accuracy than the Weibull distribution. Two other good candidates are the Nakagami and the Rice distributions, which can be interpreted as particular cases of the Weibull distribution for particular choices of the shape and scale parameters. These findings hold not only when predicting next-point values of the wind speed but also when predicting the wind energy values. Finally, we discuss such findings in the context of wind power forecasting and monitoring for power-grid assessment.
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