A comparison of alternative rate estimators in some frequently used growth models

This paper deals with the linear, exponential and Gompertz models and compares the bias and variance of a number of estimators of the growth-rate parameters of these models. Some of these estimators have been commonly recommended in the literature and others are most frequently used in empirical practice. The present analysis points to the strengths and weaknesses of the estimators in their usage.     

On additive and multiplicative damage models and the characterizations of linear and logarithmic exponential families

Rao (1963) has formulated a damage model which we call an additive damage model. A suitable damage model, which we call a multiplicative damage model, has been considered by Krishnaji (1970) for income-related problems. In these models, an original observation is subjected to damage, e.g., death or under-reporting, according to a specified probability law. Within the framework of an additive damage model, with a special form of damage, characterizations of the linear and logarithmic exponential families are formulated using regression properties of the damaged part on the undamaged part. The characterizations of the gamma and Pareto distributions that have been found of some use in the theory of income distributions, are obtained as special cases. Similar results are investigated within the framework of the multiplicative damage model.     

On random variate generation for the generalized hyperbolic secant distributions

We give random variate generators for the generalized hyperbolic secant distribution and related families such as Morris's skewed generalized hyperbolic secant family and a family introduced by Laha and Lukacs. The rejection method generators are uniformly fast over the parameter space and are based upon a complex function representation of the distributions due to Harkness and HarknessThe author's research was sponsored by NSERC Grant A3456 and FCAR Grant 90-ER-0291.     

论指数函数及其四则运算的并行算法

本文用指数函数建立双曲函数的并行串行最新算法     

ESTIMATION OF GUARANTEE TIME AND MEAN LIFE AFTER WARRANTY FOR TWO-PARAMETER EXPONENTIAL FAILURE MODEL

Suppose manufactured items have failure times distributed with the two-parameter exponential density function à-^le-(x-μ)/à (x≥μ≥0). The paper considers estimation of the guarantee time μ and mean life after warranty à. Properties of various estimators are given for both separate and simultaneous estimation of μ and à. Criteria for comparing estimators are entropy loss, LINEX loss, and (generalized) Pitman nearness.     

Slice sampling for simulation based fitting of spatial data models

An auxiliary variable method based on a slice sampler is shown to provide an attractive simulation-based model fitting strategy for fitting Bayesian models under proper priors. Though broadly applicable, we illustrate in the context of fitting spatial models for geo-referenced or point source data. Spatial modeling within a Bayesian framework offers inferential advantages and the slice sampler provides an algorithm which is essentially off the shelf. Further potential advantages over importance sampling approaches and Metropolis approaches are noted and illustrative examples are supplied.     

Multiparameter estimation of discrete exponential distributions

Let X₁, …, X_p be independent random variables, all having the same distribution up to a possibly varying unspecified parameter, where each of the p distributions belongs to the family of one parameter discrete exponential distributions. The problem is to estimate the unknown parameters simultaneously. Hudson (1978) shows that the minimum variance unbiased estimator (MVUE) of the parameters is inadmissible under squared error loss, and estimators better than the MVUE are proposed. Essentially, these estimators shrink the MVUE towards the origin. In this paper, we indicate that estimators shifting the MVUE towards a point different from the origin or a point determined by the observations can be obtained.     

Some characterizations of distributions of the exponential-type

We consider a particular subclass of the two-parameter exponential family with natural parameters γ₁, γ₂ and characterize those distributions of the family having a ratio of the mean value and the variance that is a linear function of γ₁ by the form of the moment generating function. As special cases we find the normal and the gamma distributions.     

一类推广的Halanay不等式的稳定性研究及其应用

利用Halanay不等式的推广形式,证明了一类时滞微分系统的指数稳定性,得到了一个新的积分条件,推广和改进了已有的结果,并结合例子加以说明.     

Generalized Mixtures of Gamma and Exponentials and Reliability Properties of the Maximum from Friday and Patil Bivariate Exponential Model

The minimum and maximum order statistics from many of the common bivariate exponential distributions are predominantly generalized mixtures of exponentials; however, the maximum from the Friday and Patil bivariate exponential (FPBVE) model is either a generalized mixture of three or fewer exponentials or a generalized mixture of gamma and exponentials. In this article, we obtain conditions based on the weights and parameters of the generalized mixtures of gamma and one or two exponential distributions that yield legitimate probability models. Furthermore, we analyze properties of the failure rate of the maximum from the FPBVE model. This answers a question raised in Baggs and Nagaraja (1996 Baggs , G. E. , Nagaraja , H. N. ( 1996 ). Reliability properties of order statistics from bivariate exponential distributions . Commun. Statist. Stochastic Mod. 12 : 611 – 631 .[Taylor & Francis Online] , [Google Scholar]).