Order statistics from trivariate normal and -distributions in terms of generalized skew-normal and skew- distributions

We consider here a generalization of the skew-normal distribution, GSN(λ₁,λ₂,ρ), defined through a standard bivariate normal distribution with correlation ρ, which is a special case of the unified multivariate skew-normal distribution studied recently by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574]. We then present some simple and useful properties of this distribution and also derive its moment generating function in an explicit form. Next, we show that distributions of order statistics from the trivariate normal distribution are mixtures of these generalized skew-normal distributions; thence, using the established properties of the generalized skew-normal distribution, we derive the moment generating functions of order statistics, and also present expressions for means and variances of these order statistics.Next, we introduce a generalized skew-t_ν distribution, which is a special case of the unified multivariate skew-elliptical distribution presented by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574] and is in fact a three-parameter generalization of Azzalini and Capitanio's [2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. Roy. Statist. Soc. Ser. B 65, 367–389] univariate skew-t_ν form. We then use the relationship between the generalized skew-normal and skew-t_ν distributions to discuss some properties of generalized skew-t_ν as well as distributions of order statistics from bivariate and trivariate t_ν distributions. We show that these distributions of order statistics are indeed mixtures of generalized skew-t_ν distributions, and then use this property to derive explicit expressions for means and variances of these order statistics.     

Semiparametric estimation for count data through weighted distributions

This paper is concerned with semiparametric discrete kernel estimators when the unknown count distribution can be considered to have a general weighted Poisson form. The estimator is constructed by multiplying the Poisson estimate with a nonparametric discrete kernel-type estimate of the Poisson weight function. Comparisons are then carried out with the ordinary discrete kernel probability mass function estimators. The Poisson weight function is thus a local multiplicative correction factor, and is considered as the uniform measure to detect departures from the equidispersed Poisson distribution. In this way, the effects of dispersion and zero-proportion with respect to the standard Poisson distribution are also minimized. This method of estimation is also applied to the weighted binomial form for the count distribution having a finite support. The proposed estimators, in addition to being simple, easy-to-implement and effective, also outperform the competing nonparametric and parametric estimators in finite-sample situations. Two examples illustrate this new semiparametric estimation.     

Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics

In this article, we introduce three new distribution-free Shewhart-type control charts that exploit run and Wilcoxon-type rank-sum statistics to detect possible shifts of a monitored process. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of these charts is that, due to their nonparametric nature, the false alarm rate (FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the charts for some typical FAR values. Furthermore, a numerical study carried out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations.     

ASSOCIATIONS BETWEEN AIR POLLUTION AND HOSPITAL VISITS FOR CARDIOVASCULAR DISEASES IN THE ELDERLY IN SYDNEY USING BAYESIAN STATISTICAL METHODS

Using generalized linear models (GLMs), Jalaludin  et al. (2006;  J. Exposure Analysis and Epidemiology   16 , 225–237) studied the association between the daily number of visits to emergency departments for cardiovascular disease by the elderly (65+) and five measures of ambient air pollution. Bayesian methods provide an alternative approach to classical time series modelling and are starting to be more widely used. This paper considers Bayesian methods using the dataset used by Jalaludin  et al.  (2006) , and compares the results from Bayesian methods with those obtained by Jalaludin  et al.  (2006) using GLM methods.     

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

The variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with Gaussian observation densities illustrate this. If the variational algorithm is initialized with a large number of hidden states, redundant states are eliminated as the method converges to a solution, thereby leading to a selection of the number of hidden states. In addition, through the use of a variational approximation, the deviance information criterion for Bayesian model selection can be extended to the hidden Markov model framework. Calculation of the deviance information criterion provides a further tool for model selection, which can be used in conjunction with the variational approach.     

17世纪前期喀尔喀右翼在西藏的活动

本文主要依据<五世达赖喇嘛传><清内阁蒙古堂档>等藏、蒙文史料,通过考察喀尔喀右翼的关键性人物阿海岱青和温布额尔德尼珲台吉在西藏的活动,探究17世纪前期喀尔喀右翼与西藏关系的历史原貌.指出在喀尔喀左翼土谢图汗部崛起之前,喀尔喀右翼在与西藏的关系中扮演着主要角色这一以往蒙藏关系研究中所忽视的史实,揭示了17世纪前期在西藏复杂的政局中蒙藏关系发展的另一端.     

Residential Remittances and Food Security in the Upper West Region of Ghana

In recent years, out migration from the Upper West Region to the southern belt of Ghana for farming has become commonplace. The natural question that has arisen is: what is the potential impact of remittances from this migration pattern on food security in the region? Using multivariate ordered logistic regression this study assesses the linkage between remittances and household food security (derived using the HFIAS) among urban and rural households (n=1,438) in the region. The findings show that urban remittance‐receiving households and rural remittance and non‐remittance receiving households were more likely (OR=2.44, p<0.05; OR=2.46, p<0.001; and OR=1.49, p<0.1, respectively) to report being more severely food‐insecure than urban non‐remittance receiving households. The findings demonstrate that household strategies such as migration and remittances on their own are not sufficient to ameliorate the precarious food insecurity situation of the region. The study calls for development of alternative livelihoods in the region.     

International Migrant Remittances and Labour Supply in Nigeria

The study analyses how remittances to Nigeria affect the labour supply of recipients using Propensity Score Matching (PSM) and a Log‐Linear regression model, with data from the 2013 Nigerian General Household Survey. The PSM results show that for the entire sample, the difference between the average amount of labour supplied per week by those that receive remittances and the amount they would have supplied without remittances is insignificant. The marginal impact analysis also shows that, ceteris paribus, the average labour supply for all recipients is inelastic to remittances. The results from the sub‐group analysis, however, show that receiving remittances negatively affects the labour supply of the self‐employed in agriculture, teenagers and the elderly. These results led us to the recommendation that policies to increase the inflow of remittances should be encouraged but in tandem with programmes to educate farmers on the benefit of investing remittances received in their farming business.