Additive Outlier Detection and Estimation for the Logarithmic Autoregressive Conditional Duration Model

This study investigates the influences of additive outliers on financial durations. An outlier test statistic and an outlier detection procedure are proposed to detect and estimate outlier effects for the logarithmic Autoregressive Conditional Duration (Log-ACD) model. The proposed test statistic has an exact sampling distribution and performs very well, in terms of size and power, in a series of Monte Carlo simulations. Furthermore, the test statistic is robust to several alternative distribution assumptions. An empirical application shows that parameter estimates without considering outliers tend to be biased.     

Some Bayesian lower bounds on reliability in the lognormal distribution

The two-parameter lognormal distribution with density function f(y: γ, σ²) = [(2πσ²)^1/2y] ¹exp[?(ln y ? γ)²/2σ²], y > 0, is important as a failure-time model in life testing. In this paper, Bayesian lower bounds for the reliability function R(t: γ, σ²) = ?[(γ ? ln t)/σ] are obtained for two cases. First, it is assumed that γ is known and σ² has either an inverted gamma or “general uniform” prior distribution. Then, for the case that both γ and σ² are unknown, the normal-gamma prior and Jeffreys' vague prior are considered. Some Monte Carlo simulations are given to indicate some of the properties of the Bayesian lower bounds.     

Robustness of the linear discriminant function to nonnormality: Johnson's system

The asymptotic distribution of the Errors of Misclassification in using the Linear Discriminant Function is investigated here. The purpose is to study the effects of nonnormality on these errors. The class of distributions considered is the Johnson's system. Each of the three random variables can be transformed to normality. In one particular case numerical evaluations are made, based on which it is possible to recommend whether or not it is necessary to make the transformation prior to classification. In a parallel study, we present similar results for the Edgeworth Series distribution, where the random variables cannot be transformed to normality.     

Inference for a Simple Step-Stress Model with Type-I Censoring and Lognormally Distributed Lifetimes

Accelerated life-testing (ALT) is a very useful technique for examining the reliability of highly reliable products. It allows the experimenter to obtain failure data more quickly at increased stress levels than under normal operating conditions. A step-stress model is one special class of ALT, and in this article we consider a simple step-stress model under the cumulative exposure model with lognormally distributed lifetimes in the presence of Type-I censoring. We then discuss inferential methods for the unknown parameters of the model by the maximum likelihood estimation method. Some numerical methods, such as the Newton–Raphson and quasi-Newton methods, are discussed for solving the corresponding non-linear likelihood equations. Next, we discuss the construction of confidence intervals for the unknown parameters based on (i) the asymptotic normality of the maximum likelihood estimators (MLEs), and (ii) parametric bootstrap resampling technique. A Monte Carlo simulation study is carried out to examine the performance of these methods of inference. Finally, a numerical example is presented in order to illustrate all the methods of inference developed here.     

万能寿险保单盈利能力分析

与传统寿险相比,万能寿险保单具有保障和投资功能、提供最低收益保证、保险利益直接与投资收益相连、保单变更灵活和产品透明等特点,进而万能保单的盈利模式也与传统寿险不同。本文对万能寿险保单的个人账户投资资产构建对数正态分布模型,计算账户价值,利用现金流法计算万能寿险保单公司账户责任准备金,进而计算公司利润水平指标,然后通过随机模拟对影响万能寿险保单盈利能力的个人账户收益率、留存收益率、公司账户投资收益率、贴现利率、生存和死亡概率等因素进行了分析。     

Lognormal Distributions for Skin Area as a Function of Body Weight1

This paper reanalyzes the dataset cited by the U.S. Environmental Protection Agency in its Exposure Factors Handbook that contains measurements of skin area, height, and body weight for 401 people spanning all stages of development. The reanalysis shows that a univariate model for total skin area as a function of body weight gives useful and practical results with little or no loss of reliability as compared to the Agency's bivariate model. This new result leads to a new method to develop Lognormal distributions for total skin area as a function of body weight alone.     

Simulation on probability points for testing of lognormal or weibull distribution with a small sample

Two extensive computer simulated tables of percentage points of the asymptotic test statistics for testing lognormal or Weibull population proposed by Pereira (1978) are discussed. Special attention is given to small sample cases. Some of the most commonly used 16 symmetrical probability points are reported. These points are 0.001, 0.005, 0.01. 002. 0.025. 0.05. 0.10.0.15, 0.85, 0.90, 0.95, 0.975, 0.98, 0.99, 0.995 and 0.999. These empirical Sumulated results can be used to test hypotheses for these two particular populations and are adequate when using a normal approximation.     

Point and block prediction in log-Gaussian random fields: The non-constant mean case

This work considers the problems of point and block prediction in log-Gaussian random fields for the case when the mean of the log-process is not constant and depends linearly on unknown parameters. First, we propose a new point predictor that is optimal within a certain family of predictors, which extend a result in De Oliveira [2006. On optimal point and block prediction in log-Gaussian random fields. Scand. J. Statist. 33, 523–540.] that holds in the case when the mean of the log-process is constant. Second, we show that the results in De Oliveira [2006. On optimal point and block prediction in log-Gaussian random fields. Scand. J. Statist. 33, 523–540.] regarding optimal block prediction cannot be extended to the case when the mean of the log-process is not constant. Specifically, we show that the two families of block predictors considered by De Oliveira lack an optimal predictor. Finally, we numerically compare the predictive efficiency of the proposed point and block predictors.     

Likelihood inference for lognormal data with left truncation and right censoring with an illustration

The lognormal distribution is quite commonly used as a lifetime distribution. Data arising from life-testing and reliability studies are often left truncated and right censored. Here, the EM algorithm is used to estimate the parameters of the lognormal model based on left truncated and right censored data. The maximization step of the algorithm is carried out by two alternative methods, with one involving approximation using Taylor series expansion (leading to approximate maximum likelihood estimate) and the other based on the EM gradient algorithm (Lange, 1995). These two methods are compared based on Monte Carlo simulations. The Fisher scoring method for obtaining the maximum likelihood estimates shows a problem of convergence under this setup, except when the truncation percentage is small. The asymptotic variance-covariance matrix of the MLEs is derived by using the missing information principle (Louis, 1982), and then the asymptotic confidence intervals for scale and shape parameters are obtained and compared with corresponding bootstrap confidence intervals. Finally, some numerical examples are given to illustrate all the methods of inference developed here.