The inverse binomial distribution as a statistical model

A particular case of Jain and Consul's (1971) generalized neg-ative binomial distribution is studied. The name inverse binomial is suggested because of its close relation with the inverse Gaussian distribution. We develop statistical properties including conditional inference of a parameter. An application using real data is given.     

Asa Advisory Committees to Federal Statistical Agencies: A Report of the Committee on Committees of the American Statistical Association

(Editor's Note: The following report on ASA advisory committees was prepared by Edwin D. Goldfield as part of a continuing study of the Association's committees and Sections being conducted by the Committee on Committees. Because of the importance of advisory committees to Federal agencies, the report is included here for the information of the members of the Association.)     

Least Squares Programs-A Look at the Square Root Procedure

Various algorithms are in use on computers to solve least squares problems. Apparently very few programs use the square root procedure. In this paper, results from programs based on the square root procedure are compared with results based on some other algorithms. Remarkably good results are obtained using the square root procedure.     

Identities and inequalities for the expected values of random matrices and loewner's theory

We consider the identity associated with the expected values of the matrix-valued quadratic forms of two random matrices. As a special case the identity yields the matrix-valued inequality of the Schwarz type. The most important application is for Loewner's theory in the context of the operator-monotone function, and the inequalities based on the concavityconvexity of the matrix-valued functions are derived.     

A Sequential Multi-Hypothesis Test for the Mean Function of a Discrete-Time Gaussian Process

Abstract

A sequential multi-hypothesis test for the mean function of a discrete-time Gaussian process with known covariance kernel is developed. It is obtained by applying the Bechhofer-Kiefer-Sobel generalized sequential probability ratio test GSPRT, and its properties are studied analytically. Selected applications to i.i.d. normal random variables, observation in a time series AR(1) model, and Wiener processes are given.     

Estimating the minimum and maximum location parameters for two ig-exponential scale mixtures

Suppose that we have two components, each having a two-parameter exponential distribution. Suppose further that these components are conditionally independent, sharing a common random hazard rate and possessing unequal, fixed, unknown location parameters. We develop estimators for the minimum and maximum of these location parameters when the random hazard rate has an inverse Gaussian distribution. Performance comparisons are made among the proposed estimators. Maximum likelihood estimators are shown to be inadmissible.     

用淬冷法确定饱和液氮中的池沸腾热流密度曲线

用直径为５０ｍｍ、厚度为１２ｍｍ的铜平板在液氮中进行了不同热面方位角的淬冷沸腾实验，各方位角为θ＝０°（热面向下）、１０°、２０°、３０°、５０°和９０°（热面垂直）；随着方位角的增加，临界热流密度、最小膜态沸腾热流密度及其壁面过热度相应地增加，且在方位角θ＜３０°时，θ对上述参数的影响更大；得出ｑＣＨＦ、ｑｍｉｎ与方位角的关系式．     

Tests for outliers in the inverse Gaussian distribution,with application to first hitting time models

The inverse Gaussian (IG) distribution is often applied in statistical modelling, especially with lifetime data. We present tests for outlying values of the parameters (μ, λ) of this distribution when data are available from a sample of independent units and possibly with more than one event per unit. Outlier tests are constructed from likelihood ratio tests for equality of parameters. The test for an outlying value of λ is based on an F-distributed statistic that is transformed to an approximate normal statistic when there are unequal numbers of events per unit. Simulation studies are used to confirm that Bonferroni tests have accurate size and to examine the powers of the tests. The application to first hitting time models, where the IG distribution is derived from an underlying Wiener process, is described. The tests are illustrated on data concerning the strength of different lots of insulating material.     

The sliced inverse regression algorithm as a maximum likelihood procedure

It is shown that the sliced inverse regression procedure proposed by Li corresponds to the maximum likelihood estimate where the observations in each slice are samples of multivariate normal distributions with means in an affine manifold.     

Random number generators for the generalized Birnbaum–Saunders distribution

The generalized Birnbaum–Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum–Saunders models are compared by using this estimation method.