Multivariate mixture modeling using skew-normal independent distributions

In this paper we consider a flexible class of models, with elements that are finite mixtures of multivariate skew-normal independent distributions. A general EM-type algorithm is employed for iteratively computing parameter estimates and this is discussed with emphasis on finite mixtures of skew-normal, skew-t, skew-slash and skew-contaminated normal distributions. Further, a general information-based method for approximating the asymptotic covariance matrix of the estimates is also presented. The accuracy of the associated estimates and the efficiency of some information criteria are evaluated via simulation studies. Results obtained from the analysis of artificial and real data sets are reported illustrating the usefulness of the proposed methodology. The proposed EM-type algorithm and methods are implemented in the R package mixsmsn.     

Testing the number of components of the mixture of two inverse Weibull distributions

In this paper, we use the likelihood ratio test (LRT) for testing the number of components in a mixture of two inverse Weibull distributions (MTIWD). First, we formulate the null distribution of the likelihood ratio statistic. Next, we calculate the percentage points of the test statistic under two different stopping criteria. In addition, we compute the power of the proposed test under these two stopping criteria and show that global maximization of the likelihood is not necessary to obtain a good power of the LRT. Finally, we discuss two applications to illustrate whether a set of data arises from a single or a MTIWD.     

一类非线性微分代数系统的能控性子分布

能控性子分布在系统的能控性分解中起着重要作用.针对一类非线性微分代数系统,利用M导数方法,提出了能控性子分布的概念.给出了一个计算包含在某些分布内的最大能控性子分布的算法,同时讨论了该算法的一些性质.最后,给出一个例子说明如何利用本文给出的算法计算此类微分代数系统的包含在某给定分布内的最大能控性子分布.     

A simple and fast algorithm for computing exponentials of power series

As was initially shown by Brent, exponentials of truncated power series can be computed using a constant number of polynomial multiplications. This note gives a relatively simple algorithm with a low constant factor.     

On power and sample size computation for multiple testing procedures

Power and sample size determination has been a challenging issue for multiple testing procedures, especially stepwise procedures, mainly because (1) there are several power definitions, (2) power calculation usually requires multivariate integration involving order statistics, and (3) expansion of these power expressions in terms of ordinary statistics, instead of order statistics, is generally a difficult task. Traditionally power and sample size calculations rely on either simulations or some recursive algorithm; neither is straightforward and computationally economic. In this paper we develop explicit formulas for minimal power and r-power of stepwise procedures as well as complete power of single-step procedures for exchangeable and non-exchangeable bivariate and trivariate test statistics. With the explicit power expressions, we were able to directly calculate the desired power, given sample size and correlation. Numerical examples are presented to illustrate the relationship among power, sample size and correlation.     

On Relations for Moments of Generalized Order Statistics for Lindley–Weibull Distribution

Moments of generalized order statistics appear in several areas of science and engineering. These moments are useful in studying properties of the random variables which are arranged in increasing order of importance, for example, time to failure of a computer system. The computation of these moments is sometimes very tedious and hence some algorithms are required. One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments. Generalized order statistics provides several models of ordered data as a special case. The moments of generalized order statistics also provide moments of order statistics and record values as a special case. In this research, the recurrence relations for single, product, inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution. These relations will be helpful for obtained moments of generalized order statistics from Lindley–Weibull distribution recursively. Special cases of the recurrence relations will also be obtained. Some characterizations of the distribution will also be obtained by using moments of generalized order statistics. These relations for moments and characterizations can be used in different areas of computer sciences where data is arranged in increasing order.     

A refined EM algorithm for PH distributions

This paper proposes an improved computation method of maximum likelihood (ML) estimation for phase-type (PH) distributions with a number of phases. We focus on the EM (expectation-maximization) algorithm proposed by Asmussen et al. [27] and refine it in terms of time complexity. Two ideas behind our method are a uniformization-based procedure for computing a convolution integral of the matrix exponential and an improvement of the forward-backward algorithm using time intervals. Compared with the differential-equation-based EM algorithm discussed in Asmussen et al. [27], our approach succeeds in the reduction of computation time for the PH fitting with a moderate to large number of phases. In addition to the improvement of time complexity, this paper discusses how to estimate the canonical form by applying the EM algorithm. In numerical experiments, we examine computation times of the proposed and differential-equation-based EM algorithms. Furthermore, the proposed EM algorithm is also compared with the existing PH fitting methods in terms of computation time and fitting accuracy.     

Stylized facts of financial time series and hidden semi-Markov models

Hidden Markov models reproduce most of the stylized facts about daily series of returns. A notable exception is the inability of the models to reproduce one ubiquitous feature of such time series, namely the slow decay in the autocorrelation function of the squared returns. It is shown that this stylized fact can be described much better by means of hidden semi-Markov models. This is illustrated by examining the fit of two such models to 18 series of daily sector returns.     

Confidence intervals of the hazard rate function for discrete distributions using mixtures

The statistical models and methods for lifetime data mainly deal with continuous nonnegative lifetime distributions. However, discrete lifetimes arise in various common situations where either the clock time is not the best scale for measuring lifetime or the lifetime is measured discretely. In most settings involving lifetime data, the population under study is not homogenous. Mixture models, in particular mixtures of discrete distributions, provide a natural answer to this problem. Nonparametric mixtures of power series distributions are considered, as for instance nonparametric mixtures of Poisson laws or nonparametric mixtures of geometric laws. The mixing distribution is estimated by nonparametric maximum likelihood (NPML). Next, the NPML estimator is used to build estimates and confidence intervals for the hazard rate function of the discrete lifetime distribution. To improve the performance of the confidence intervals, a bootstrap procedure is considered where the estimated mixture is used for resampling. Various bootstrap confidence intervals are investigated and compared to the confidence intervals obtained directly from the NPML estimates.     

An EM algorithm for estimating the parameters of bivariate Weibull distribution under random censoring

We consider the problem of estimation of the parameters of the Marshall-Olkin Bivariate Weibull distribution in the presence of random censoring. Since the maximum likelihood estimators of the parameters cannot be expressed in a closed form, we suggest an EM algorithm to compute the same. Extensive simulations are carried out to conclude that the estimators perform efficiently under random censoring.     

相关Weibull分布雷达杂波的建模与仿真

为了有效地在杂波背景下检测或处理雷达信号,介绍了零记忆非线性变换ZMNL法产生相关随机序列的方法.基于法的特点.详细分析并建立了Weibull分布的雷达杂波模型.且进行了计算机仿真.结果产生了具有高斯谱的相关Weibull分布杂渡,并给出了概率密度和功率谱密度的理论和实际仿真曲线,从而证明了方法能有效而准确地模拟雷达杂波.仿真得到的杂波序列可以直接应用到雷达环境特性的研究、雷达相干视频信号的模拟及对雷达回波信号的分析与检测.     

On transformations of formal power series

Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve recognizability, generalizing the recent results of Zhang [16] to the formal power series setting. We show, for example, that the “square-root” operation, while preserving regularity for formal languages, preserves recognizability for formal power series when the underlying semiring is commutative or locally finite, but not in general.     

Using the EM algorithm for inference in a mixture of distributions with censored but partially identifiable data

This paper describes an implementation of the EM algorithm for the statistical analysis of a finite mixture of distributions arising when data are censored but partially identifiable. We consider a scheme of type I censoring where censoring times are random. The estimation of standard errors proposed by Meng and Rubin (1991. Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. J. Amer. Statist. Assoc. 86(416), 899-909) is also implemented in the context of the above mixture. A Bayesian method introduced in Contreras-Cristán et al. (2003. Statistical inference for mixtures of distributions for censored data with partial identification. Commun. in Statist. Theory Methods 32(4), 749-774) for the case of a constant censoring value is extended to the case of random censoring times. Comparisons with different methods are carried out both with simulated data and with the observations on failure times for communication transmitter-receivers of Mendenhall and Hader (1958. Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data. Biometrika 45, 504-520).     

Skew and infinitary formal power series

We investigate finite-state systems with weights. Departing from the classical theory, in this paper the weight of an action does not only depend on the state of the system, but also on the time when it is executed; this reflects the usual human evaluation practices in which later events are considered less urgent and carry less weight than close events. We first characterize the terminating behaviors of such systems in terms of rational formal power series. This generalizes a classical result of Schützenberger.     

A New Generalized Weibull Model: Classical and Bayesian Estimation

Statistical distributions play a prominent role in applied sciences, particularly in biomedical sciences. The medical data sets are generally skewed to the right, and skewed distributions can be used quite effectively to model such kind of data sets. In the present study, therefore, we propose a new family of distributions suitable for modeling right-skewed medical data sets. The proposed family may be called a new generalized-X family. A special sub-model of the proposed family called a new generalized-Weibull distribution is discussed in detail. The maximum likelihood estimators of the model parameters are obtained. A brief Monte Carlo simulation study is conducted to evaluate the performance of these estimators. Finally, the proposed model is applied to the remission times of the stomach cancer patient’s data. The comparison of the goodness of fit results of the proposed model is made with the other competing models such as Weibull, Kumaraswamy Weibull, and exponentiated Weibull distributions. Certain analytical measures such as Akaike information criterion, Bayesian information criterion, Anderson Darling statistic, and Kolmogorov–Smirnov test statistic are considered to show which distribution provides the best fit to data. Based on these measures, it is showed that the proposed distribution is a reasonable candidate for modeling data in medical sciences and other related fields.     

Processes as formal power series: A coinductive approach to denotational semantics

We characterize must testing equivalence on CSP in terms of the unique homomorphism from the Moore automaton of CSP processes to the final Moore automaton of partial formal power series over a certain semiring. The final automaton is then turned into a CSP-algebra: operators and fixpoints are defined, respectively, via behavioural differential equations and simulation relations. This structure is then shown to be preserved by the final homomorphism. As a result, we obtain a fully abstract compositional model of CSP phrased in purely set-theoretical terms.     

Applications of power series in computational geometry

A number of algorithms are presented for obtaining power series expansions of curves and surfaces at a point. Some results on the radius of convergence are given. Two applications of series are given:

1. • for curve tracing algorithms, where a truncated series is used to approximate the curve of intersection of two surfaces

2. • to define nth degree geometric continuity, for arbitrary

A comparative study of nonparametric estimation in Weibull regression: A penalized likelihood approach

The Weibull distribution is popularly used to model lifetime distributions in many areas of applied statistics. This paper employs a penalized likelihood method to estimate the shape parameter and an unknown regression function simultaneously in a nonparametric Weibull regression. Four methods were considered: two cross-validation methods, a corrected Akaike information criterion, and a Bayesian information criterion. Each method was evaluated based on shape parameter estimation as well as selecting the smoothing parameter in a penalized likelihood model through a simulation study. Adapting a lower-dimensional approximation and deriving confidence intervals from Bayes models of the penalized likelihood, the comparative performances of methods using both censored and uncensored data were examined for various censoring rates. The methods are applied to a real data example of lung cancer.     

基于改进遗传算法的电力系统无功优化的研究

电力系统无功优化问题是一个多变量、多约束的混合非线性规划问题,其操作变量既有连续变量又有离散变量,其优化过程比较复杂。遗传算法是模拟生物在自然环境中的遗传和进化过程而形成的一种自适应的全局优化搜索算法,可用于解决含有离散变量的复杂优化问题。本文选用遗传算法求解电力系统无功优化问题,并对基本遗传算法的编码、初始种群、适应度函数和交叉、变异策略等进行改进,使用本文提出的改进算法对IEEE1 4节点进行无功优化计算,结果证明本文模型和算法的实用性、可靠性和优越性。