On a Class of Distributions Defined by the Relationship Between Their Density and Distribution Functions

Knowledge concerning the family of univariate continuous distributions with density function f and distribution function F defined through the relation f(x) = F ^α(x)(1 ? F(x))^β, α, β ? , is reviewed and modestly extended. Symmetry, modality, tail behavior, order statistics, shape properties based on the mode, L-moments, and—for the first time—transformations between members of the family are the general properties considered. Fully tractable special cases include all the complementary beta distributions (including uniform, power law and cosine distributions), the logistic, exponential and Pareto distributions, the Student t distribution on 2 degrees of freedom and, newly, the distribution corresponding to α = β = 5/2. The logistic distribution is central to some of the developments of the article.     

Probability density function of quotient of order statistics from the pareto,power and weibull distributions

This paper deals with the probability density functions of quotient of order statistics. We use the Mellin transform technique, to find the distribution of the quotient Z= X/Xwhere X.,X(i < j) are the ith and jth order statistics from the Pareto, Power and Weibull distributions     

A simple way to obtain the spectral decomposition of variance components models for balanced data

By means of an example it is shown how eigenvalues and eigenvectors of variance components models can be obtained straightforwardly when balanced data are available. Simple asymptotically efficient estimators of the variance components are presented.     

Bayesian autoregressive spectral analysis

The article describes an operational Bayesian approach to making inferences for the spectral density function for univariate autoregressive processes and for the AR operator of multivariate autoregressive processes. The derivation of the approach is described. Numerical examples, including the Wolfer Sunspot numbers, are used to demonstrate the practical usefulness of the approach.     

Limited information bayesian analysis of a structural coefficient in a simultaneous equations system

An analytical expression is obtained for the marginal posterior density for a structural coefficient in a simultaneous equations system based on a limited information Bayesian analysis. A con- ditional posterior density is obtained given reduced form para- meters. This conditional posterior density is in univariate student t form. Numerical examples suggest that the conditional density hasa tighter distribution around the posterior mean than the unconditional density when the correlation between the endo- genous variables and the structural error term is high.     

A new special class of peb designs

A new class of partially efficiency-balanced designs is introduced from a practical point of view. This new design includes all equireplicated incomplete block designs available in literature as special cases. The fundamental properties of the design are clarified with relation to other block designs.     

Automatic selection of a linear predictor through frequency domain cross-validation

Given data from a weakly stationary stochastic process in discrete time, and any L-step ahead linear predictor estimated from that data, we will construct an approximately unbiased estimator of the resulting mean squared error of L-step ahead linear prediction. The motivation for the estimator is based on frequency domain cross-validation, and hence the range of validity and applicability of the resulting selection method is not limited by particular assumptions about the structure of the underlying stochastic process or the form of the fitted linear predictors. We also propose a new frequency domain predictor fitting method. The method provides a natural finite-past analog to the existing spectral factorization techniques, and it compares favorably with the existing techniques, both asymptotically and for finite samples. In a Monte Carlo study, we compare several predictor selection methods, at lead times one and five. The performance criterion used is the mean squared prediction error of the selected predictor. The new selection methods work well, and a comparison of results for the two different lead times underscores the need for tailoring the selection criterion to suit the lead time.     

A survey of statistical methods on remote sensing in russian literature from 1976 to 1985

In this article we review the major areas of remote sensing in the Russian literature for the period 1976 to 1985 that use statistical methods to analyze the observed data. For each of the areas, the problems that have been studied and the statistical techniques that have been used are briefly described