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Invariant transformations to combine marginal probability functions to form multivariate distributions motivated by the need to enlarge the class of multivariate distributions beyond the multivariate normal distribution and its related functions such as the multi- variate Student's t-distribution and the Wishart distribution. An example is Frank's family of bivariate distributions. (The word 'copula' comes from Latin and means to connect or join.) Quintessentially copulas are measures of the dependent structure of the marginal distributions and they have been used to model correlated risks, joint default probabilities in credit portfolios and groups of individuals that are exposed to similar economic and physical environments. Also used in frailty models for surveying.
Pascal's triangle is an arrangement of numbers described by Pascal in his Traité du Triangle Arithmétique published in the year 1665 as 'The number in each cell is equal to in the
How is the rejection region defined and how is that related to the z-score and the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians
Kleiner Hartigan trees is a technique for displaying the multivariate data graphically as the 'trees' in which the values of the variables are coded into length of the terminal br
A test for equality of the variances of the two populations having normal distributions, based on the ratio of the variances of the sample of observations taken from each. Most fre
Chernoff's faces : A method or technique for representing the multivariate data graphically. Each observation is represented by the computer-created face, the features of which are
Baddeley'smetric : A manner of measuring the 'error' in the image processing technique or method. The metric is derived using the fundamental theory from the stochastic geometry an
Chance events : According to the Cicero these are events which occurred or will occur in ways which are the uncertain-events which may happen, may not happen, or may happen in some
Normality - Reasons for Screening Data Prior to analyzing multivariate normality, one should consider univariate normality Histogram, Normal Q-Qplot (values on x axis
Lorenz curve : Essentially the graphical representation of cumulative distribution of the variable, most often used for the income. If the risks of disease are not monotonically in
Described by the leading proponent as 'the conscientious, explicit, and judicious uses of present best evidence in making the decisions about the care of individual patients, and
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