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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.
Personal probabilities : A radically special approach for allocating probabilities to events than, for instance, the commonly used long-term relative frequency approach. In this ty
National lotteries : Games of chance held to heave money for particular causes. The first held in the UK took place in the year 1569 principally to raise money for repair of the Ci
Confidence interval : A range of the values, calculated from the sample observations which is believed, with the particular probability, to posses the true parameter value. A 95% c
Recursive models are the statistical models in which the causality flows in one direction, that is models which include only unidirectional effects. Such type of models do not inc
Indirect standardization is the procedure of adjusting the crude mortality or morbidity rate for one or more variables by making use of a known reference population. It may, for in
Bayes factor : A summary of evidence for the modelM1 against the another modelM0 provided by the set of data D, which can be used in the model selection. Given by the ratio of post
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
The generalization of the normal distribution used for the characterization of functions. It is known as a Gaussian process because it has Gaussian distributed finite dimensional m
Chi-squared distribution : It is the probability distribution, f (x), of the random variable de?ned as the sum of squares of the number (v) of independent standard normal variables
Generalized principal components analysis: The non-linear version of the principal components analysis in which the goal is to determine the non-linear coordinate system which is
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