Inference for the common mean of several Birnbaum–Saunders populations

The Birnbaum–Saunders distribution is a widely used distribution in reliability applications to model failure times. For several samples from possible different Birnbaum–Saunders distributions, if their means can be considered as the same, it is of importance to make inference for the common mean. This paper presents procedures for interval estimation and hypothesis testing for the common mean of several Birnbaum–Saunders populations. The proposed approaches are hybrids between the generalized inference method and the large sample theory. Some simulation results are conducted to present the performance of the proposed approaches. The simulation results indicate that our proposed approaches perform well. Finally, the proposed approaches are applied to analyze a real example on the fatigue life of 6061-T6 aluminum coupons for illustration.     

Comparison of several Birnbaum–Saunders distributions

Birnbaum–Saunders (BS) distribution is widely used in reliability applications to model failure times. For several samples from possible different BS distributions, to prevent wrong conclusions in any further analysis, it is of importance to accompany a formal comparison for characteristic quantities of the distributions, including mean, quantile and reliability function difference. To this end, two test statistics, which are respectively based on the exact generalized p-value approach and the Delta method, are proposed and their behaviours are investigated. Simulation studies are carried out to examine the size and power performance of the newly proposed statistics. An interesting phenomenon is that in the finite sample simulations we conduct, the Delta method-based test almost uniformly outperforms the generalized p-value-based test although its sampling null distribution is simulated by Monte Carlo method. This might suggest that the sampling null distribution of the Delta method-based test statistic would have a fast convergence to its limit. The tests are also applied to analyse a real example on the fatigue life of 6061-T6 aluminium coupons for illustration.     

Generalized Inverse Gamma Distribution and its Application in Reliability

In this article, we introduce a new reliability model of inverse gamma distribution referred to as the generalized inverse gamma distribution (GIG). A generalization of inverse gamma distribution is defined based on the exact form of generalized gamma function of Kobayashi (1991). This function is useful in many problems of diffraction theory and corrosion problems in new machines. The new distribution has a number of lifetime special sub-models. For this model, some of its statistical properties are studied. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. We also demonstrate the usefulness of this distribution on a real data set.     

Some statistical opportunities in the agricultural sciences

Quantitative plant-disease epidemiology gained its primary motivation with the publication of VanderPlank's (1963) mathematical treatise, since which a range of predominantly deterministic models has been proposed by plant pathologists to describe the temporal dynamic of plant diseases. In this article, a number of results are reviewed. In particular, a summary is made of the primary models developed in the literature together with diseases for which they were proposed; estimation of the infection rate is considered for the generalized logistic model; and a bivariate stochastic model for stem and leaf infection is developed and used to obtain measures of plant disease stress.     

EM algorithm-based likelihood estimation for a generalized Gompertz regression model in presence of survival data with long-term survivors: an application to uterine cervical cancer data

In this paper we develop a regression model for survival data in the presence of long-term survivors based on the generalized Gompertz distribution introduced by El-Gohary et al. [The generalized Gompertz distribution. Appl Math Model. 2013;37:13–24] in a defective version. This model includes as special case the Gompertz cure rate model proposed by Gieser et al. [Modelling cure rates using the Gompertz model with covariate information. Stat Med. 1998;17:831–839]. Next, an expectation maximization algorithm is then developed for determining the maximum likelihood estimates (MLEs) of the parameters of the model. In addition, we discuss the construction of confidence intervals for the parameters using the asymptotic distributions of the MLEs and the parametric bootstrap method, and assess their performance through a Monte Carlo simulation study. Finally, the proposed methodology was applied to a database on uterine cervical cancer.     

人民币汇率与地区差距 ——人民币国际化的视角

 本文分析了人民币汇率对国内地区差距产生影响的两种传导机制，即对外商品贸易和外国直接投资两种渠道。为检验此结论，将全国分为东、中、西和东北四大地区，计算Theil系数得到地区差距的指标体系；再结合人民币的实际有效汇率，利用滞后阶数扩展VAR模型(LA-VAR)的方法进行实证分析，得到结论：人民币汇率对国内地区差距具有显著格兰杰影响，广义脉冲响应函数的分析还进一步揭示了影响的方向。这说明，人民币汇率波动对各地区的冲击具有非对称性，基于Grauwe(2003)的研究：人民币版图内的货币体系运行具有较高的净成本。在此现状下急于推进人民币国际化，是缺乏稳健性的。     

The gamma-linear failure rate distribution: theory and applications

For any continuous baseline G distribution, Zografos and Balakrishnan [On families of beta- and generalized gamma-generated distributions and associated inference. Statist Methodol. 2009;6:344–362] introduced the generalized gamma-generated distribution with an extra positive parameter. A new three-parameter continuous model called the gamma-linear failure rate (LFR) distribution, which extends the LFR model, is proposed and studied. Various structural properties of the new distribution are derived, including some explicit expressions for ordinary and incomplete moments, generating function, probability-weighted moments, mean deviations and Rényi and Shannon entropies. We estimate the model parameters by maximum likelihood and obtain the observed information matrix. The new model is modified to cope with possible long-term survivors in lifetime data. We illustrate the usefulness of the proposed model by means of two applications to real data.     

双重广义线性模型在车损险费率厘定中的应用

双重广义线模型是对广义线性模型的扩展,其对反应变量的均值与散度参数同时建立模型,提高了模型运用的灵活性与适应性。将双重广义线性模型应用到车损险费率厘定中,既考虑了费率期望值与费率因子之间的关系,又考虑了变量的分散程度与费率因子之间的关系,并以欧洲一家保险公司的汽车保险损失数据为样本进行实证研究,把无索赔优待等级、地区、车型与年均行驶里程数作为费率因子,建立了费率厘定模型。结果表明,所得到费率结构合理,符合实际。     

On a recent generalization of gamma distribution

In this paper, we investigate a generalized gamma distribution recentIy developed by Agarwal and Kalla (1996). Also, we show that such generalized distribution, like the ordinary gamma distribution, has a unique mode and, unlike the ordinary gamma distribution, may have a hazard rate (mean residual life) function which is upside-down bathtub (bathtub) shaped.     

Ergodicity of generalized Ait-Sahalia-type interest rate model

In this paper, we consider sufficient conditions for the stationary distribution of generalized Ait-Sahalia-type interest rate model. We show that if r ? 2ρ ? 1, then the generalized Ait-Sahalia interest rate model has a unique stationary distribution and if r < 2ρ ? 1, then the generalized Ait-Sahalia interest rate model is recurrent relative to the domain (0, ?), for any ? > 0. Besides, some recursion formulas for the stationary distribution are presented. Finally, some numerical simulations are used to illustrate our results.     

Antipodally symmetric distributions for orientation statistics

The conventional antipodally symmetric Bingham matrix distribution on the Stiefel manifold is generalized. Large sample maximum likelihood estimation and uniformity tests are discussed, and a parametric model for axial orientations (X-shapes) is suggested. A generalization of the Khatri-Mardia matrix distribution is developed to provide a model suitable for hybrids (T-shapes).     

Adjusting and Comparing Survival Curves by Means of an Additive Risk Model

Survival curves may be adjusted for covariates using Aalen's additive risk model. Survival curves may be compared by taking the ratio of two adjusted survival curves; the ratio is denoted the generalized relative survival rate. Adjusting both survival curves for all but one of a common set of covariates gives the partial relative survival rate, which measures the covariate-specific contribution to the generalized relative survival rate. The generalized and partial relative survival rates have interpretations similar to the traditional relative survival rates frequently used in cancer epidemiology. In fact, the traditional relative survival rate can be generalized to a regression context using the additive risk model. This population-adjusted relative survival rate is an alternative and useful method for removing confounding effects of age, cohorts, and sex. The authors use a data set of malignant melanoma patients diagnosed from 1965 to 1974 in Norway. The 25-year survival of 1967 individuals is studied.     

On diagnostic devices for proposing half-logistic and inverse half-logistic models using generalized (k) record values

In this work we consider the generalized upper (k) record values (GURV’s) and generalized lower (k) record values (GLRV’s) arising from half-logistic distribution (HLD) and inverse half-logistic distribution (IHLD). We derive some characterization results of HLD based on some moment relations of generalized upper (k) record values and those of generalized lower (k) record values and accordingly devised some diagnostic tools to identify HLD as a model to the distribution of a population. Similar characterization theorems and diagnostic tools are developed for IHLD as well. Simulation studies are conducted to validate the diagnostic tools devised for both HLD and IHLD.     

Model selection of the generalized von Mises distribution based on empirical mode decomposition with data analyses

This paper presents a method for selecting a distribution within the generalized von Mises (GvM) class. In this method, the logarithmic form of the GvM probability frequency function is regarded as the sum of a constant and several cosine functions with different frequencies. Based on the empirical mode decomposition (EMD) method, the corresponding logarithmic series is decomposed to several intrinsic mode functions (IMF) whose corresponding instantaneous frequencies (IF) are used to be the basis of the GvM model selection. The applications of the proposed method are illustrated using simulated circular data and real wind direction data. The results demonstrate that the method proposed here can provide a good choice for the GvM model selection.     

Optimal record-based statistical procedures for the two-parameter exponential distribution

There are a number of situations in which the experimental data observed are record statistics. In this paper, optimal confidence intervals as well as uniformly most powerful (MP) tests for one-sided alternatives are developed. Since a uniformly MP test for a two-sided alternative does not exist, generalized likelihood ratio and uniformly unbiased and invariant tests are derived for the two parameters of the exponential distribution based on record data. For illustrative purposes, a data set on the times between consecutive telephone calls to a company's switchboard is analysed using the proposed procedures. Finally, some open problems in this direction are pointed out.     

Use of non-normality in structural equation modeling: Application to direction of causation

Structural equation modeling (SEM) typically utilizes first- and second-order moment structures. This limits its applicability since many unidentified models and many equivalent models that researchers would like to distinguish are created. In this paper, we relax this restriction and assume non-normal distributions on exogenous variables. We shall provide a solution to the problems of underidentifiability and equivalence of SEM models by making use of non-normality (higher-order moment structures). The non-normal SEM is applied to finding the possible direction of a path in simple regression models. The method of (generalized) least squares is employed to estimate model parameters. A test statistic for examining a fit of a model is proposed. A simulation result and a real data example are reported to study how the non-normal SEM approach works empirically.     

An efficient procedure for computing minque of variance components and generalized least squares estimates of fixed effects

An efficient method for computing minimum norm quadratic unbiased estimates (MINQUE) of variance components and generalized least squares estimates of the fixed effects in the mixed model is developed. The computing algorithm uses a modification of the W transformation.     

Transformed symmetric generalized autoregressive moving average models

Cordeiro and Andrade [Transformed generalized linear models. J Stat Plan Inference. 2009;139:2970–2987] incorporated the idea of transforming the response variable to the generalized autoregressive moving average (GARMA) model, introduced by Benjamin et al. [Generalized autoregressive moving average models. J Am Stat Assoc. 2003;98:214–223], thus developing the transformed generalized autoregressive moving average (TGARMA) model. The goal of this article is to develop the TGARMA model for symmetric continuous conditional distributions with a possible nonlinear structure for the mean that enables the fitting of a wide range of models to several time series data types. We derive an iterative process for estimating the parameters of the new model by maximum likelihood and obtain a simple formula to estimate the parameter that defines the transformation of the response variable. Furthermore, we determine the moments of the original dependent variable which generalize previous published results. We illustrate the theory by means of real data sets and evaluate the results developed through simulation studies.     

Geiger Counter-Type Pólya–Eggenberger Distributions

Motivated by the paper of Dandekar (1955), a one-urn model with Polya–Eggenberger sampling scheme is developed, which yields a large number of discrete distributions, including the Dandekar's modified binomial distribution, as particular cases. The model is further modified to some new generalized distributions of order k. Some probable applications of these models were discussed in Dandekar (1955) and Feller (1968) in fields of fertility study and radioactivity. It also has applications in premium determination in insurance sector.