A Recursive Formula for the Probability of Occurrence of at Least m out of N Events

A recursive same-sign relation is derived that reduces the probability of occurrence of at least m out of N independent events to the probability of occurrence of at least m out of N ? 1 of these N events.     

Random sampling from the watson distribution

An envelope-rejection method is used to generate random variates from the Watson distribution. The method is compact and is competitive with, if not superior to, the existing sampling algorithms. For the girdle form of the Watson distribution, a faster algorithm is proposed. As a result, Johnson's sampling algorithm for the Bingham distribution is improved.     

A class of semiparametric transormation frailty models with application to estimating treatment effects and heterogenity in aids clinical traials

Muitivariate failure time data are common in medical research; com¬monly used statistical models for such correlated failure-time data include frailty and marginal models. Both types of models most often assume pro¬portional hazards (Cox, 1972); but the Cox model may not fit the data well This article presents a class of linear transformation frailty models that in¬cludes, as a special case, the proportional hazards model with frailty. We then propose approximate procedures to derive the best linear unbiased es¬timates and predictors of the regression parameters and frailties. We apply the proposed methods to analyze results of a clinical trial of different dose levels of didansine (ddl) among HIV-infected patients who were intolerant of zidovudine (ZDV). These methods yield estimates of treatment effects and of frailties corresponding to patient groups defined by clinical history prior to entry into the trial.     

The asymptotic distribution of a pivotal quantity for a capture-recapture model

A pivotal quantity for a capture-recapture model is introduced and used to construct an asymptotic confidence region for (ε,N), where ε is the capture efficiency and N is the population size. The true confidence levels of certain regions are obtained by simulation. Certain confidence regions for (ε,N) are drawn to show the size of the regions and to show how confidence limits for N depend on ε.     

Robustness of testing the equality of two slopes in simple linear structural relationships

The usual test of the equality of two slopes in a simple structural relation-ship is the test formed from the normal approximation using the Fisher information matrix, assuming two explanatory variables are independent. This paper examines the robustness if the explanatory variables are, in fact, dependent. A more efficient estimator is derived for a matched pair situation.     

Portmanteau test for conditional heteroscedasticity, using ranks of squared residuals

Squared residual autocorrelations have been found useful in detecting departures from linearity in time series models. This is especially the case with data exhibiting heterogeneity in variances. A rank test is proposed which is much more robust than its parametric counterpart.