A note on the joint distribution of correlated quadratic forms

In the present paper, the authors obtained exact and asymptotic expressions for the joint distribution of correlated quadratic forms when the underlying distribution is a multivariate normal.     

TESTING THE EQUALITY OF PARAMETERS IN THE DISTRIBUTIONS WHEN THE RANGE DEPENDS UPON THE PARAMETER

The authors derive the null and non-null distributions of the test statistic v=y_min/y_max (where y_min= min x_ij, y_max= max x_ij, J=1,2, …, k) connected with testing the equality of scale parameters θ₁, θ₂, …θ_k in certain, class of density functions given by      

On estimation of the mean parameter of a truncated normal disiribution with known coefficient of variation

This paper eals with the proplem on estimating the mean paramerer of a truncated normal distribution with known coefficient of variation. In the previous treatment of this problem most authors have used the sample standared deviation for estimating this parameter. In the present paper we use Gini’s coefficient of mean difference g and obtain the minimum variance unbiased estimate of the mean based on a linear function of the sample mean and g, It is shown that this new estimate has desirable properties for small samples as well as for large samples. We also give a numerical example.     

Usability of Online Services: The Role of Technology Readiness and Context*

An important prerequisite for the success of any online service is ensuring that customers' experience—via the interface—satisfies both sensory and functional needs. Developing interfaces that are responsive to customers' needs requires a perspective on interface design as well as a deep understanding of the customers themselves. Drawing upon research in consumer behavior concerning consumer beliefs about technology, we deploy an alternative way to describe customers based on psychographic characteristics. Technology readiness (TR), a multidimensional psychographic construct, offers a way to segment online customers based upon underlying positive and negative technology beliefs. The core premise of this study is that the beliefs form the foundation for expectations of how things should work and how specific online service interfaces are evaluated by customers. At the same time, usability evaluations of specific online services might be contingent on contextual factors, specifically the type of site (hedonic vs. utilitarian) and access method (Web vs. wireless Web). The aspects of usability examined here are those incorporated into the usability metric and instrument based on the Microsoft Usability Guidelines (MUG). The results of an empirical study with 160 participants indicate that (i) TR customer segments vary in usability requirements and (ii) usability evaluations of specific online service interfaces are influenced by complex interactions among site type, access method, and TR segment membership. As organizations continue to expand their online service offerings, managers must recognize that the interface exists to serve the customers, so their design must be matched to market needs and TR.     

Study of redundancy of vector variables in canonical correlations

Fujikoshi (1982) obtained the necessary and sufficient conditions for the increased number of variables in the two sets of vectors not affecting the original nonzero canonical correlations and used these to obtain the likelihood ratio test procedure. He assumed a nonsingular covariance matrix due to random variables. Here, we study the same problem when the covariance matrix is singular and establish some further results. In this study, we note that the unit canonical correlations have to be separated in some of the situations. These results are valid for complex random vector variables and in some situations, the test for redundancy is given for complex random variables.     

Interval estimation of the common mean

Brown and Cohen (1974) considered the problem of interval estimation of the common mean of two normal populations based on independent random samples. They showed that if we take the usual confidence interval using the first sample only and centre it around an appropriate combined estimate of the common mean the resulting interval would contain the true value with higher probability. They also gave a sufficient condition which such a point estimate should satisfy. Bhattacharya and Shah (1978) showed that the estimates satisfying this condition are nearly identical to the mean of the first sample. In this paper we obtain a stronger sufficient condition which is satisfied by many point estimates when the size of the second sample exceeds ten.     

Multivariate discrete exponential family of distributions and their properties

The paper generalizes the univariate discrete exponential family of distributions to the multivariate situation, and this generalization includes the multivariate power series distributions, the multivariate Lagrangian distributions, and the modified multivariate power-series distributions. This provides a unified approach for the study of these three classes of distributions. We obtain recurrence relations for moments and cumulants, and the maximum likelihood estimation for the discrete exponential family. These results are applied to some multivariate discrete distributions like the Lagrangian Poisson, Lagrangian (negative) multinomial, logarithmic series distributions and multivariate Lagrangian negative binomial distribution.     

Analysis of incomplete data in experiments with repeated measurements in clinicaltrials using a stochastic model

A stochastic model is proposed to analyze the observation vectors of variable lengths in a long-term clinical trial. Using a Markovian normal density, the likelihood ratio tests for usual hypotheses are derived and asymptotic distributions of the test statistics are obtained. The use of 'step-down' procedure is discussed for the interim analysis and a numerical example is given to illustrate the methodology.     

Estimation of the common location paeameters for the two linear models

Various estimators proposed for the estimation of a common mean are extended to the estimation of the common location parameters for two linear models including the estimators based on preliminary tests of equality of variances. Exact distribution of these estimates, simultaneous confidence bounds based on these estimates and the bounds on the variances of these estimates are obtained using different approaches.