On the optimality of the sample variance

The present paper explores the structure of linear exponential families for which the sample variance is a uniformly minimum variance unbiased estimator.     

On the Construction of Nearest–Neighbour Balanced Row–Column Designs

Nearest–neighbour balance is considered a desirable property for an experiment to possess in situations where experimental units are influenced by their neighbours. This paper introduces a measure of the degree of nearest–neighbour balance of a design. The measure is used in an algorithm which generates nearest–neighbour balanced designs and is readily modified to obtain designs with various types of nearest–neighbour balance. Nearest–neighbour balanced designs are produced for a wide class of parameter settings, and in particular for those settings for which such designs cannot be found by existing direct combinatorial methods. In addition, designs with unequal row and column sizes, and designs with border plots are constructed using the approach presented here.     

On Unimodal Regression in the Exponential Family

In this article, we discuss statistical methods for curve-estimation under the assumption of unimodality for variables with distributions belonging to the two-parameter exponential family with known or constant dispersion parameter. An important special case is a one-parameter distribution. We suggest a nonparametric method based on monotonicity properties. The method is applied to Swedish data on laboratory verified diagnoses of influenza and data on inflation from an episode of hyperinflation in Bulgaria.     

On some moving-average processes with exponentially distributed innovations

Summary In this paper we discusse the stationary sequence of random variables which are formed from an independent identically distributed sequence, according to the moving-average model of ordern. Some properties of the process are considered. The joint bivariate exponential distribution is given, as well as the distribution of the sum.     

Note on sums of a random number of random variables with exponential family distributions

With the help of the result that exponential-type families are determined by their mean value functions it is shown that stochastic independence of the random variables S_N and N-S_N characterizes the Poisson and Bernoulli distributions simultaneously.     

On Unbiased Estimation of Positive Integral Powers of the Natural Parameter in Exponential Families

We explore the structure of one‐parameter exponential families admitting an unbiased estimator for a positive integral power of the natural parameter. It is seen that only exponential families dominated by Lebesgue measure can have this property. It is outlined that similar results can be obtained for other functions of the natural parameter.     

指数族分布中参数的经验贝叶斯估计

指数族分布是一类应用广泛的分布类,包括了泊松分布、Gamma分布、Beta分布、二项分布等常见分布.在非寿险中,索赔额或索赔次数过程常常被假定服从指数族分布,由于风险的非齐次性,指数族分布中的参数θ也为随机变量,假定服从指数族共轭先验分布.此时风险参数的估计落入了Bayes框架,风险参数θ的Bayes估计被表达“信度”形式.然而,在实际运用中,由于先验分布与样本分布中仍然含有结构参数,根据样本的边际分布的似然函数估计结构参数,从而获得风险参数的经验Bayes估计,最后证明了该经验Bayes估计是渐近最优的.     

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.     

A Note on the Arithmetic—Geometric—Harmonic Mean Inequalities

The familiar inequalities relating the arithmetic, geometric, and harmonic means are derived as corollaries to likelihood ratio tests.     

On the fisher β-sufficient partition

This paper shows that the Fisher information in a partition of the space of a random variable X is less than or equal to the Fisher information of X about the unknown parameter. It also provides tables to construct β-sufficient partitions if X has an exponential distribution or a geometric distribution. Simulation study was conducted to show the advantage of using these tables over the usual methods used to construct histograms.     

A Characterization of probability densities with expected log likelihood

In the class of all densities with constraints E b_i(X) = c,(i = 1,....,q), it is well known that the entropy is maximized by the density belonging to the exponential family specified by b_i(x), i = 1,....,q. Our aim in this note is to generalize theresult by using expected log likelihood.     

A new family of lifetime models

We introduce a new family of distributions by adding a parameter to the Marshall–Olkin family of distributions. Some properties of the new family of distributions are derived. A particular case of the family, a three-parameter generalization of the exponential distribution, is given special attention. The shape properties, moments, distributions of the order statistics, entropies and estimation procedures are derived. An application to a real data set is discussed.     

The Poisson-conjugate Lindley mixture distribution

ABSTRACT

A new discrete distribution that depends on two parameters is introduced in this article. From this new distribution the geometric distribution is obtained as a special case. After analyzing some of its properties such as moments and unimodality, recurrences for the probability mass function and differential equations for its probability generating function are derived. In addition to this, parameters are estimated by maximum likelihood estimation numerically maximizing the log-likelihood function. Expected frequencies are calculated for different sets of data to prove the versatility of this discrete model.     

On a geometrical derivation of the upper tail of the null distribution of w-exponential

Shapiro and Wilk (1972) proposed a goodness of fit test for the exponential distribution. Carrie (1980) obtained an explicit expression of the null distribution of their test statistic W (n) E in a neighbourhood of its upper tail. His derivation uses a certain transformation involving the order statistics from the standard exponential distribution. In this paper we present an alternative derivation of this distribution using an elementary geometrical argument.     

Likelihood

This article reviews some recent work on large-sample likelihood inference, in particular work related to conditional inference and ancillary statistics. The background discussion includes a relation between conditional inference and testing for model fit. There are brief comments on results for sequential estimation, also on the difficulties associated with multiparameter problems.     

Mixture of the Riesz Distribution with Respect to a Multivariate Poisson

The aim of this article is to study a statistical model obtained by the mixture of the Riesz probability distribution on symmetric matrices with respect to a multivariate Poisson distribution. We show that this distribution is related to the modified Bessel function of the first kind. We then determine the domain of the means and the variance function of the generated natural exponential family.     

Multivariate stable exponential families and Tweedie scale

In this paper, we characterize the multivariate stable natural exponential families by a property of homogeneity of the cumulant function of some basis, and by a property of homogeneity of the variance function. We also extend the definition of a Tweedie scale to a finite dimensional space and we give a class of natural exponential families belonging to this scale on the space of symmetric matrices.     

On the moments of record values

In this paper some general relations for expectations of functions of record values are established. It is seen that these relations may be used to obtain recurrence relations for moments of record values. Bounds on expectations of record values with numerical computations are presented. Applications to the characterizations of the generalizeed exponential distribution are also given.