Some developments on the log-Dagum distribution

Skewed and fat-tailed distributions frequently occur in many applications. Models proposed to deal with skewness and kurtosis may be difficult to treat because the density function cannot usually be written in a closed form and the moments might not exist. The log-Dagum distribution is a flexible and simple model obtained by a logarithmic transformation of the Dagum random variable. In this paper, some characteristics of the model are illustrated and the estimation of the parameters is considered. An application is given with the purpose of modeling kurtosis and skewness that mark the financial return distribution.      

Parameter estimation for mixtures of skew Laplace normal distributions and application in mixture regression modeling

In this article, we propose mixtures of skew Laplace normal (SLN) distributions to model both skewness and heavy-tailedness in the neous data set as an alternative to mixtures of skew Student-t-normal (STN) distributions. We give the expectation–maximization (EM) algorithm to obtain the maximum likelihood (ML) estimators for the parameters of interest. We also analyze the mixture regression model based on the SLN distribution and provide the ML estimators of the parameters using the EM algorithm. The performance of the proposed mixture model is illustrated by a simulation study and two real data examples.     

A Note on “Shaved Dice” Inference

Two dice are rolled repeatedly, only their sum is registered. Have the two dice been “shaved,” so two of the six sides appear more frequently? Pavlides and Perlman discussed this somewhat complicated type of situation through curved exponential families. Here, we contrast their approach by regarding data as incomplete data from a simple exponential family. The latter, supplementary approach is in some respects simpler, it provides additional insight about the relationships among the likelihood equation, the Fisher information, and the EM algorithm, and it illustrates the information content in ancillary statistics.     

Doubly reweighted estimators for the parameters of the multivariate t-distribution

The t-distribution (univariate and multivariate) has many useful applications in robust statistical analysis. The parameter estimation of the t-distribution is carried out using maximum likelihood (ML) estimation method, and the ML estimates are obtained via the Expectation-Maximization (EM) algorithm. In this article, we will use the maximum Lq-likelihood (MLq) estimation method introduced by Ferrari and Yang (2010 Ferrari, D., and Y. Yang. 2010. Maximum lq-likelihood estimation. The Annals of Statistics 38 (2):753–83.[Crossref], [Web of Science ®] , [Google Scholar]) to estimate all the parameters of the multivariate t-distribution. We modify the EM algorithm to obtain the MLq estimates. We provide a simulation study and a real data example to illustrate the performance of the MLq estimators over the ML estimators.     

SURVIVAL ANALYSIS WITH TIME DEPENDENT FRAILTY USING A LONGITUDINAL MODEL

A method of estimation for generalised mixed models is applied to the estimation of regression parameters in a proportional hazards model with time dependent frailty. A parameter representing change over time is introduced and is modelled in turn into a fixed effect, a normally distributed random effect and a longitudinal effect in which the random component relates to the patient characteristics. Both maximum likelihood and residual maximum likelihood estimators are given.     

碳约束下江苏省节能减排效率时空演化及分异研究

节能减排是发展低碳经济，建设生态文明的必由之路。运用ＤＥＡ 的ＧＭＬ 指数法和Ａ?ＥＢＭ法相结合的创新模式测算有碳约束下２００６—２０１４ 年江苏省地级市节能减排效率。结果表明：江苏省节能减排效率均值为０?? ８２９，９ 年间整体上升２?? ０％，其中Ａ?ＥＢＭ 效率呈“Ｗ”型变化，ＧＭＬ 指数的变化呈现波动向上的“Ｍ”型；空间区域分布特点为苏南地区领先、苏中次之、苏北地区相对落后。