Tables of the cumulative non-central chi-square distribution-part 6 (finish)

The cumulative non-central chi-square distribution is tabulated for all combinations of values of α=0(0.1) 1.0 (0.2)3.0(0.5)5.0(1.0)34.0,v=1(1)30(2)50(5)100 and y=0.01 (0.01)0.1(0.1)1.0(0.2)3.0(0.5)10.0(1.0 30.0(2.0)50.0(5.0)165.0. The computations have been correctly rounded to five decimal places. Also, there is a discussion about the error involved in the computations. Furthermore, there is a discussion about possible interpolation in the table using the Lagrange's method     

On the linear combinations of the means of inverse gaussian distributions

Consider the two parameter Inverse Gaussian distribution with mean μ and scale parameter λ.

Suppose one is interested in testing a problem on a linear combination for the means of Inverse Gaussian distributions. For this problem a test and confidence intervals are proposed when: (1) λ’s are known and; (2) λ’s are unknown.

Finally an application of the procedures is illustrated with a data set of failure times of high-speed turbine bearings.     

Current and past roles of the statistician in space applications

The paper contains a brief and informal history of space science topics which led to statistical consulting. The past and current roles of the statistician in space science is discussed and this special issue is prefaced by describing generally the contents of the issue. Several statistical problems associated with the space scientists’ efforts to develop instrumentation and space vehicles for both manned and unmanned space missions are discussed as well as those problems associated with developing a space laboratory. The current tasks of developing remote sensors to make earth observations for monitoring earth resources and the associated statistical problems are also discussed. These latter activities are those that have motivated this special issue.     

Fourth Quarter Survey of the Economic Outlook

Written mainly for its pedagogical interest, this note deals with the computational formulas for the recursive updating of weighted least squares parameter estimates and the residual sum of squares in the general linear model under the assumption that the errors have a multivariate normal distribution. This approach simplifies considerably the derivations of Haslett (1985).     

Some inadmissibility results for estimating ordered uniform scale parameters

Independent random samples (of possibly unequal sizes) are drawn from k (≥2) uniform populations having unknown scale parameters μ₁,…,μ_k. The problem of componentwise estimation of ordered parameters is investigated. The loss function is assumed to be squared error and the cases of known and unknown ordering among μ₁,…,μ_k. are dealt with separately. Sufficient conditions for an estimator to be inadmissible are provided and as a consequence, many natural estimators are shown to be inadmissible, Better estimators are provided.     

The growth curve model: a review

A survey is given of papers which have influenced or have been influenced by the Growth Curve Model due to Potthoff & Roy (1964). The review covers, among others, methods of estimating parameters, the canonical version of the model, tests, extensions, incomplete data, Bayesian approaches and covariance structures.     

Robust analysis of variance

The classes of R- and M-estimates contain practical robust alternatives to least squares estimation in linear models. These estimates form the basis for a robust analysis of variance. This inference procedure is described and its versatility demonstrated.     

On optimal tests for general interval-hypotheses

Optimal statistical tests, using the normality assumptions for general interval hypotheses including equivalence testing and testing for nonzero difference (or for non-unit) are presented. These tests are based on the decision theory for Polya Type distributions and are compared with usual confidence tests and with ’two one-sided tests’- procedures. A formal relationship between some optimal tests and the Anderson and Hauck procedure as well as a procedure recommended by Patel and Gupta is given. A new procedure for a generalisation of Student's test as well as for equivalence testing for thet-statistics is shown.     

A new formula for the computation of multivariate factorized moments by using the joint cumulative distribution function

This work presents a closed formula to compute any muitivariate factorized expected value from the knowledge of the joint cumulative distribution function (cdf) of any random variable. Additionally, a new nonparametric estimator alternative to the sample average is presented for the univariate case.     

Finite sample moments of a bootstrap estimator of the james-stein rule

The finite sample moments of the bootstrap estimator of the James-Stein rule are derived and shown to be biased. Analytical results shed some light upon the source of bias and suggest that the bootstrap will be biased in other settings where the moments of the statistic of interest depends on nonlinear functions of the parameters of its distribution.