Lagrange Multiplier Tests for Normality Against Seminonparametric Alternatives

In this article, I derive the Lagrange multiplier test of the null hypothesis that a stationary random vector has a (possibly heteroscedastic) normal distribution against the alternative that the distribution is a member of the family with seminonparametric probability density functions considered by Gallant and Tauchen (1989). The test is shown to contain special cases of the moment tests proposed by Newey (1985) and Tauchen (1985). Evidence from a small simulation study is reported, showing that the test has reasonable finite-sample properties in moderately sized samples. The test is applied to the change of price in a treasury-bill data series analyzed by Tauchen and Pitts (1983) and Tauchen (1985).     

基于ANSYS二次开发求解实体单元内力在港口工程中的应用

在依据规范对混凝土块体进行配筋计算时,需要求得该块体的内力。而有些混凝土块体结构非常不规则,一般采用有限元软件进行计算。当采用有限元软件ANSYS对复杂结构进行分析时,需要采用实体单元。而ANSYS软件不能直接输出实体单元的内力图,需要进行二次开发。介绍了力学中将应力转为内力的计算原理,并应用于ANSYS二次开发中求解实体单元的内力。结合实际工程,求出了实体单元的弯矩图和扭矩图。结果表明,此求解实体单元内力图程序具有很好的适用性和通用性,可以应用于ANSYS分析港口工程中。     

Interval estimation of the negative binomial dispersion parameter

Inference concerning the negative binomial dispersion parameter, denoted by c, is important in many biological and biomedical investigations. Properties of the maximum-likelihood estimator of c and its bias-corrected version have been studied extensively, mainly, in terms of bias and efficiency [W.W. Piegorsch, Maximum likelihood estimation for the negative binomial dispersion parameter, Biometrics 46 (1990), pp. 863–867; S.J. Clark and J.N. Perry, Estimation of the negative binomial parameter κ by maximum quasi-likelihood, Biometrics 45 (1989), pp. 309–316; K.K. Saha and S.R. Paul, Bias corrected maximum likelihood estimator of the negative binomial dispersion parameter, Biometrics 61 (2005), pp. 179–185]. However, not much work has been done on the construction of confidence intervals (C.I.s) for c. The purpose of this paper is to study the behaviour of some C.I. procedures for c. We study, by simulations, three Wald type C.I. procedures based on the asymptotic distribution of the method of moments estimate (mme), the maximum-likelihood estimate (mle) and the bias-corrected mle (bcmle) [K.K. Saha and S.R. Paul, Bias corrected maximum likelihood estimator of the negative binomial dispersion parameter, Biometrics 61 (2005), pp. 179–185] of c. All three methods show serious under-coverage. We further study parametric bootstrap procedures based on these estimates of c, which significantly improve the coverage probabilities. The bootstrap C.I.s based on the mle (Boot-MLE method) and the bcmle (Boot-BCM method) have coverages that are significantly better (empirical coverage close to the nominal coverage) than the corresponding bootstrap C.I. based on the mme, especially for small sample size and highly over-dispersed data. However, simulation results on lengths of the C.I.s show evidence that all three bootstrap procedures have larger average coverage lengths. Therefore, for practical data analysis, the bootstrap C.I. Boot-MLE or Boot-BCM should be used, although Boot-MLE method seems to be preferable over the Boot-BCM method in terms of both coverage and length. Furthermore, Boot-MLE needs less computation than Boot-BCM.     

A reformulation of the criteria for the independence of quadratic functions in normal variables

The Craig-Sakamoto theorem establishes a sufficient and necessary condition for the independence of two quadratic forms in normal variates, fascinating many statisticians and mathematicians, who continuously seek for simple and better proofs of the theorem and its extensions. In this article, we present a simple proof of a unified theorem on the independence of linear and quadratic functions in general normal variates.     

Equine-assisted social work counteracts self-stigmatisation in self-harming adolescents and facilitates a moment of silence

The purpose of this study was to determine whether equine-assisted social work (EASW) could affect self-stigmatisation and thereby counteract false identities in self-harming adolescents. Data were collected via interviews with nine female self-harming clients aged 15–21 years and eight staff members. Interviews and video-recorded human–horse interactions with three staff members and four clients were analysed. The interviews were followed by further dialogue with participants while they viewed videos of their own EASW sessions. The analysis indicated that the horse had a calming effect on the clients; enabled them to free themselves of their preoccupations; provided real-time, non-verbal and non-judgmental feedback on their emotions; and increased feelings of trust, patience and empathy. The presence of a horse provided a ‘moment of silence’ for the clients, silencing their inner critic, and made them feel more authentic and better able to regulate their emotions. However, staff could counteract this ‘safe’ healing by being too focused on goals, making interpretations and lecturing and encouraging clients, thus making clients feel judged anyhow. EASW seemed to give clients the opportunity to break free from self-stigmatisation, which seemed to lower the barrier to change.     

A new class of weighted exponential distributions

Introducing a shape parameter to an exponential model is nothing new. There are many ways to introduce a shape parameter to an exponential distribution. The different methods may result in variety of weighted exponential (WE) distributions. In this article, we have introduced a shape parameter to an exponential model using the idea of Azzalini, which results in a new class of WE distributions. This new WE model has the probability density function (PDF) whose shape is very close to the shape of the PDFS of Weibull, gamma or generalized exponential distributions. Therefore, this model can be used as an alternative to any of these distributions. It is observed that this model can also be obtained as a hidden truncation model. Different properties of this new model have been discussed and compared with the corresponding properties of well-known distributions. Two data sets have been analysed for illustrative purposes and it is observed that in both the cases it fits better than Weibull, gamma or generalized exponential distributions.     

Comparison of estimation methods for the Weibull distribution

Weibull distributions have received wide ranging applications in many areas including reliability, hydrology and communication systems. Many estimation methods have been proposed for Weibull distributions. But there has not been a comprehensive comparison of these estimation methods. Most studies have focused on comparing the maximum likelihood estimation (MLE) with one of the other approaches. In this paper, we first propose an L-moment estimator for the Weibull distribution. Then, a comprehensive comparison is made of the following methods: the method of maximum likelihood estimation (MLE), the method of logarithmic moments, the percentile method, the method of moments and the method of L-moments.     

中国保险公司下侧风险状况研究——基于下端部分矩的实证分析

下端部分矩(LPM)是量度下侧风险的有效工具。本文将下侧风险的量度运用于我国保险业的实证研究,以资产收益率(ROA)作为收益指标,通过对比香港上市的三家保险公司在投资者不同风险偏好下的下端部分矩(LPM)的值,定量分析我国保险上市公司面临的风险状况,为进一步实现保险公司投资者的风险和收益最优权衡以及强化保险公司内部监管提供有效的工具。     

A new extended generalized Gompertz distribution with statistical properties and simulations

Abstract

Statistical distributions are very useful in describing and predicting real world phenomena. In many applied areas there is a clear need for the extended forms of the well-known distributions. Generally, the new distributions are more flexible to model real data that present a high degree of skewness and kurtosis. The choice of the best-suited statistical distribution for modeling data is very important.

In this article, we proposed an extended generalized Gompertz (EGGo) family of EGGo. Certain statistical properties of EGGo family including distribution shapes, hazard function, skewness, limit behavior, moments and order statistics are discussed. The flexibility of this family is assessed by its application to real data sets and comparison with other competing distributions. The maximum likelihood equations for estimating the parameters based on real data are given. The performances of the estimators such as maximum likelihood estimators, least squares estimators, weighted least squares estimators, Cramer-von-Mises estimators, Anderson-Darling estimators and right tailed Anderson-Darling estimators are discussed. The likelihood ratio test is derived to illustrate that the EGGo distribution is better than other nested models in fitting data set or not. We use R software for simulation in order to perform applications and test the validity of this model.     

Exact inference for the two-parameter exponential distribution under Type-II hybrid censoring

Epstein (1954) introduced the Type-I hybrid censoring scheme as a mixture of Type-I and Type-II censoring schemes. Childs et al. (2003) introduced the Type-II hybrid censoring scheme as an alternative to Type-I hybrid censoring scheme, and provided the exact distribution of the maximum likelihood estimator of the mean of a one-parameter exponential distribution based on Type-II hybrid censored samples. The associated confidence interval also has been provided. The main aim of this paper is to consider a two-parameter exponential distribution, and to derive the exact distribution of the maximum likelihood estimators of the unknown parameters based on Type-II hybrid censored samples. The marginal distributions and the exact confidence intervals are also provided. The results can be used to derive the exact distribution of the maximum likelihood estimator of the percentile point, and to construct the associated confidence interval. Different methods are compared using extensive simulations and one data analysis has been performed for illustrative purposes.