Cumulants of random sum distributions

Consider a random variable S being the sum of a number N of independent and identically distributed random variables X_j (j = 1, 2, ...) where the number N is itself a non-negative integer-valued random variable independent of the X_j An explicit expression of the r-th cumulant of S is given in terms of the cumulants of N and X_j, Asymptotic properties of the distribution of S are also discussed.     

A two-sample parametric group sequential procedure for monitoring clinical trials

A group sequential procedure is presented which allows for staggered entry of patients, random loss to followup, and utilizes the flexible boundary approach of Lan and DeMets. The proposed procedure assumes that response times are nearly exponentially distributed. An example as well as simulation studies comparing the performance of the proposed procedure with the group sequential logrank are also presented.     

Bayes estimators of the average failure rates

In the present paper we have proposed a Bayesian approach for making inferences from accelerated life tests which do not require distributional assumptions     

Bhattacharyya distance based linear discriminant function for stationary time series

The problem of classifying a covariance stationary normal time series is considered. Under certain regularity conditions, a compact form of the linear discriminant function in the sense of maximizing the Bhattacharyya distance is obtained.     

A note on maximum Z-scores for control charts for individuals

Control chart limits are often constructed retrospectively based on a sequence of individual measurements. It is shown that the usual control chart limits cannot be crossed for small numbers of measurements.     

Characterizations of the poisson process using,the variance

Let γ(t) be the residual life at time t of the renewal process {A(t), t > 0}, which has F as the common distribution function of the inter-arrival times. In this article we prove that if Var(γ(t)) is constant, then F will be exponentially or geometrically distributed under the assumption F is continuous or discrete respectively. An application and a related example also are given.     

A nonparametric bayesian approach to analysis of drug dependence data

In this paper, a nonparametric Bayesian approach to the analysis of binary response data is considered. Using a Dirichlet process prior, and squared error loss, the Bayes estimators of response probabilities are obtained. Finally, the results obtained are employed to analyze the ARC 090 Trial data.     

Estimating the discovery rate in a continuous time recapture model

We consider a family of marked Poisson process models for the discovery of distinct errors in a computer program and also for sampling, in continu-ous time, a population containing an unknown number of distinct biological species. Captures (selections or discoveries) are assumed to occur at a con-stant rate, each event consisting of the discovery of a distinct process (error or species) or the recurrence of a previously discovered process. Using a generalization of Nayak’s (1988) model we derive confidence limits for the discovery rate. The limits are based on the asymptotic distribution of a scaled logarithmic function of the maximum likelihood estimator.     

On L 1-consistency of kernel-type density estimator for stationary markov processes

A convergence result for kernel type density estimators, proved by Devroye and Gyrofi (1985), is extended to stationary Markov processess satisfying (G ₂-condition introduced by Rosenblatt (1970).     

Extension to higher dimensions of the jaeschke-eicker result on the standardized empirical process

The asymptotic distribution of the sup-norm of the heavily weighted empirical process is established in the multidimensional case. This theorem extends in particular the famous result in Jaeschke (1975, 1979) to higher dimensions. There is a striking difference between the behaviour for higher dimensions and that for dimension one, especially the limiting distribution is now a simple transformation of a standard exponential random variable.