Mathematical forms of the distribution of the product of two normal variables

This paper finds the mathematical forms of the distribution of the product where x and x follow a bivariate normal distribution In this paper the distribution when PT0 is expressed as an integral, a new, fundamental result. From this general form, six different cases can be distinguished depending on what is known about the parameters and p. The special cases are Aroian $year:1959 and (6) Additionally, we prove that if and as the distribution of the product approaches the Type III distribution. When p=0# Aroian $year:1959 and Aroian and Meeker $year:1977, give tables for various values of 6., 6 . The results in this paper will be used to provide brief tables for p^O in a separate paper     

A multivariate solution of the multivariate ranking and selection problem

The problem of selection of the best multivariate population is given a new formulation which does not involve reducing the populations to univariate quantities. This formulation's solution is developed for known, and (using the Heteroscedastic Method) also for unknown, variance-covariance matrices. Preference reversals and arbitrary nonlinear preference functions are explicitly allowed in this new theory     

Characterization of the quantitative-qualitative measure of inaccuracy for discrete generalized probability distributions

A characterization of the quantitative-qualitative measure of inaccuracy depending upon the additivity postulate and the mean value property for discrete generalized probability distribution has been provided.     

Comparison of experiments based on generalized entropy measures

Taneja (1989) studied a unified (r,s)-entropy which includes as a particular case some of the known entropies. Based on this unified (r, s)entropys we have defined the average amount of information provided by an experiment X over the unknown parameter 8 with prior knowledge p(0). By using average amount of information in unified form, we have compared experiments based on bayesian approach. Some connections with the criteria of Blackwell and Lehmann are also made.     

Generalized Symmetric Divergence Measures and the Probability of Error

There are three classical divergence measures exist in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber (Jeffreys, 1946 Jeffreys , H. ( 1946 ). An invariant form for the prior probability in estimation problems . Proc. Roy. Soc. Lon. Ser. A 186 : 453 – 461 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Kullback and Leibler, 1951 Kullback , S. , Leibler , R. A. ( 1951 ). On information and sufficiency . Ann. Math. Statist. 22 : 79 – 86 .[Crossref] , [Google Scholar]) J-divergence. Sibson-Burbea-Rao (Sibson, 1969 Sibson , R. ( 1969 ). Information radius . Z. Wahrs. und verw Geb. 14 : 149 – 160 .[Crossref], [Web of Science ®] , [Google Scholar]), Jensen-Shannon divegernce, (Burbea and Rao, 1982 Burbea , J. , Rao , C. R. ( 1982 ). On the convexity of some divergence measures based on entropy functions . IEEE Trans. Inform. Theor. IT-28 : 489 – 495 .[Crossref], [Web of Science ®] , [Google Scholar]), and Taneja (1995 Taneja , I.J. ( 1995 ). New developments in generalized information measures , In: Hawkes , P. W. , Ed., Advances in Imaging and Electron Physics . 91:37–136 . [Google Scholar]). Arithmetic-Geometric divergence. These three measures bear an interesting relationship among each other. The divergence measures like Hellinger (1909 Hellinger , H. ( 1909 ). Neue Begründung der theorie der quadratischen formen von unendlichen vielen Veränderlichen . J. Reine Aug. Math. 136 : 210 – 271 .[Crossref] , [Google Scholar]) discrimination, symmetric χ²-divergence, and triangular discrimination are also known in the literature. In this article, we have considered generalized symmetric divergence measures having the measures given above as particular cases. Bounds on the probability of error are obtained in terms of generalized symmetric divergence measures. Study of bounds on probability of error is extended for the difference of divergence measures.     

Care and community revalued during the COVID‐19 pandemic: A feminist couple perspective

The COVID‐19 pandemic led us to understand and revalue care ethics within our daily lives and communities based on the feminist theory of care ethics. This article is a personal reflection of an academic couple living in Japan as we reflect on our experiences and the challenges encountered in caring for ourselves and our community. We discuss the ideas of care theory mainly: caring‐about and caring‐for, interchangeably in our discussion across the three‐stage categories: Home — A Commonplace; Care Ethics in Community; and Care Ethics for Self. Through these personal narratives, we strive to recognize the struggles of living through the pandemic in a virtually connected world that often disconnects us from self. We foster the idea of embracing care ethics as a starting point at an individual level.     

The impact of gender quotas on corporate boards: a cross-country comparative study

Journal of Management and Governance - Drawing on institutional theory and resource dependence theory, this study examines whether mandating gender quotas for corporate boards is associated with a...