Maximum penalized likelihood estimation for skew-normal and skew-t distributions

The skew-normal and the skew-t distributions are parametric families which are currently under intense investigation since they provide a more flexible formulation compared to the classical normal and t distributions by introducing a parameter which regulates their skewness. While these families enjoy attractive formal properties from the probability viewpoint, a practical problem with their usage in applications is the possibility that the maximum likelihood estimate of the parameter which regulates skewness diverges. This situation has vanishing probability for increasing sample size, but for finite samples it occurs with non-negligible probability, and its occurrence has unpleasant effects on the inferential process. Methods for overcoming this problem have been put forward both in the classical and in the Bayesian formulation, but their applicability is restricted to simple situations. We formulate a proposal based on the idea of penalized likelihood, which has connections with some of the existing methods, but it applies more generally, including the multivariate case.     

Point and Interval Estimation for Bivariate Normal Distribution Based on Progressively Type-II Censored Data

ABSTRACT

The maximum likelihood estimates (MLEs) of parameters of a bivariate normal distribution are derived based on progressively Type-II censored data. The asymptotic variances and covariances of the MLEs are derived from the Fisher information matrix. Using the asymptotic normality of MLEs and the asymptotic variances and covariances derived from the Fisher information matrix, interval estimation of the parameters is discussed and the probability coverages of the 90% and 95% confidence intervals for all the parameters are then evaluated by means of Monte Carlo simulations. To improve the probability coverages of the confidence intervals, especially for the correlation coefficient, sample-based Monte Carlo percentage points are determined and the probability coverages of the 90% and 95% confidence intervals obtained using these percentage points are evaluated and shown to be quite satisfactory. Finally, an illustrative example is presented.     

具有混合边界条件的地下水污染模型的特征有限元方法

本文研究了地下水污染理论中的一类带混合边界条件的非线性耦合方程组的特征有限元方法，构造模型的特征有限元全离散格式，且利用椭圆投影，建立了计算格式在Ｈ＾１模下的最佳阶误差估计，并给出了数值算例及结果分析。     

初探兔室旁核对心肌收缩力的调控

采用电刺激兔下丘脑室旁核后观察血流动力学的变化，初步探讨中枢神经系统对心肌力调控的机理。发现室旁核被刺激兴奋后，不但有升高动脉血压的作用，更重要的是对心脏有正性肌力的作用并同时增加心肌氧耗量，其机制可能与室旁核内NMDA受体的激活有关。     

Probability of Exporting Infected Carcasses from Vaccinated Pigs Following a Foot‐and‐Mouth Disease Epidemic

Emergency vaccination is an effective control strategy for foot‐and‐mouth disease (FMD) epidemics in densely populated livestock areas, but results in a six‐month waiting period before exports can be resumed, incurring severe economic consequences for pig exporting countries. In the European Union, a one‐month waiting period has been discussed based on negative test results in a final screening. The objective of this study was to analyze the risk of exporting FMD‐infected pig carcasses from a vaccinated area: (1) directly after final screening and (2) after a six‐month waiting period. A risk model has been developed to estimate the probability that a processed carcass was derived from an FMD‐infected pig (P_carc). Key variables were herd prevalence (P_H), within‐herd prevalence (P_A), and the probability of detection at slaughter (P_SL). P_H and P_A were estimated using Bayesian inference under the assumption that, despite all negative test results, ≥1 infected pigs were present. Model calculations indicated that P_carc was on average 2.0 × 10^?5 directly after final screening, and 1.7 × 10^?5 after a six‐month waiting period. Therefore, the additional waiting time did not substantially reduce P_carc. The estimated values were worst‐case scenarios because only viraemic pigs pose a risk for disease transmission, while seropositive pigs do not. The risk of exporting FMD via pig carcasses from a vaccinated area can further be reduced by heat treatment of pork and/or by excluding high‐risk pork products from export.     

A new approach to variance component estimation with diagnostic implications

Closed form expressions are developed for the estimators of functions of the variance components in balanced, mixed, linear models. These estimators are averages of sample covariances (variances) which offer diagnostic information on the data and the model. The cause of negative estimates may be revealed. Examples illustrate the basic concepts.     

Simultaneous inferences for variance ratios of some mixed linear models

Earlier investigations used a one-sided inequality to consltuct confidence regions for the variance ratios or balanced randoiu models. In this study, confidence regions are based on a two-sided generalisation of this inequality and the results are illustrated by estimating the parameters of some elementary random models.     

DECOMPOSITIONS OF THE QUEUE LENGTH DISTRIBUTIONS IN THE MAP/G/1 QUEUE UNDER MULTIPLE AND SINGLE VACATIONS WITH N-POLICY

In this paper, we establish an explicit form of matrix decompositions for the queue length distributions of the MAP/G/1 queues under multiple and single vacations with N-policy. We show that the vector generating function Y (z) of the queue length at an arbitrary time and X (z) at departures are decomposed into Y (z) = p _idle (z)ζ _Y (z) and X (z) = p _idle (z)ζ _X (z) where p _idle (z) is the vector generating function of the queue length at an arbitrary epoch at which the server is not in service, and ζ _Y (z) and ζ _X (z) are unidentified matrix generating functions.     

Compliance of the Token-Bucket Model with Markovian Traffic

Abstract

Recently, risk processes have been analyzed as fluid queues. That approach is adapted here to the analysis of the token bucket model for Markovian traffic patterns. This paper presents the Laplace transform of the time until a given traffic pattern is not compliant anymore with a particular token bucket model.     

The three-parameter two-piece normal family of distributions and its fitting

This note introduces a family of skew and symmetric distributions containing the normal family and indexed by three parameters with clear meanings. Another respect in which this family compares favourably with families like the Pearson family, the Bessel-Gram-Charlier family and the Johnson family is ease of maximum likelihood fitting. Fitting by the method of moments is also considered. Asymptotic distributions of maximum likelihood and moment estimators are worked out. A test of symmetry and normality is suggested.