An extension of bayesian measure of information to regression

This paper extends Lindley's measure of average information to the linear model, E(Y∣ß) = Xß. An expression which quantifies the average amount of information provided by the nxl vector of observations Y about the pxl vector of coefficient parameters ß will be derived. The effect of the structure of the regressor matrix, X, on the information measure is discussed. An information theoretic optimal design is characterized. Some applications are suggested.     

Large sample estimation and prediction for explosive growth curve models

Asymptotic distributions of maximum likelihood estimators for the parameters in explosive growth curve models are derived. Limit distributions of prediction errors when the parameters are estimated are also obtained. The growth curve models are viewed as multivariate time-series models, and the usual time-series methods are used for prediction. Estimation constrained by a hypothesis of homogeneity of growth rates is also considered.     

Computing the probability of hash table/urn overflow

We analyze the probability of a random distribution of n balls into m urns of size b resulting in no overflows. This solves the computational problem associated with a classical combinatorial extreme-value distribution. The problem arose during the analysis of a technique, called perfect hashing, for organizing data in computer files. The results and techniques presented can be used to solve several problems in the analysis of hashing techniques     

On the use of the scholz-sievers method for dlstribution-free inference about the difference in slopes of two regression lines

A simple adaptation of a distribution-free method due to Scholz (1978) and Sievers (1978) for inference in a single regression setting is proposed for inference about the difference in slopes of two regression lines. We assume that the data are obtained from a designed experiment with common regression constants. A comparison of the proposed method to its competitors-one due to Hollander and the other due to Rao and Gore-indicates superiority of the new method.     

Normal approximation in an urn model with indistinguishable balls

For the Bose-Einstein Statistics, where n indistinguishable balls are distributed in m urns such that all the arrangements are equally likely, define the random variables

M_k = number of urns containing exactly k balls each;

N_k = number of urns containing at least k balls each.

We consider the approximation of the distributions of M_k and N_k by suitable normal distributions, for large but finite m. Estimates are found for the error in the approximation to both the probability mass function and the distribution function in each case. These results apply also to the alternative model where no urn is allowed to be empty. The results are illustrated by some numerical examples.     

Estimation of parameters of mixed failure time distribution

The problem of estimation of parameters of a mixture of degenerate and exponential distributions is considered. A new sampling scheme is proposed and the exact bias and the mean square error (MSE) of the maximum likelihood estimators of the parameters is derived. Moment estimators, their approximate biases and the MSE are obtained. Asymptotic distributions of the estimators are also obtained for both the cases.     

A note on the operating characteristic curve of the known sigma single sampling variables plan

The operating characteristic curves of certain known sigma variables sampling plans may not be satisfactory in that they have a tendency to reject even lots of acceptable quality. This note presents the theory and a method to identify such known sigma variables plans possessing unsatisfactory operating characteristic curves.     

Lot sensitive double sampling plan (lsdsp)

A sampling plan is derived for compliance testing providing consumer protection.