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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.
Multi-hit model is the model for a toxic response which results from the random occurrence of one or the more fundamental biological events. A response is supposed to be induced o
Zero sumgame is a game played by the number of persons in which the winner takes all stakes given by the losers so that the algebraic sum of gains at any stage is zero. Number of
A two-step distillation and mixing process is shown in the figure. The system operates at steady-state conditions and there are no chemical reactions. The known flow rates and comp
Martingale: In the gambling context the term at first referred to a system for recouping losses by doubling the stake after each loss has occured. The modern mathematical concept
Duck Lovers Unlimited (DLU) Inc. assembles specially configured light jet aircrafts for airborne duck hunting. The quarterly demand forecasts for the upcoming fiscal year are:
Hazard regression is the procedure for modeling the hazard function which does not depend on the suppositions made in Cox's proportional hazards model, namely that the log-hazard
The probability distribution, f (x), of largest extreme can be given as The location parameter, α is the mode and β is the scale parameter. The mean, variance skewn
The problematic and enigmatic theory of an inference introduced by the Fisher, which extracts a probability distribution for the parameter on the basis of the data without having f
Models for the analysis of the survival times, or the time to event, data in which it is expected that a fraction of the subjects will not experience the event of interest. In a cl
The procedures used for determining how the quality of life is affected by the environment, in particular by factors such as air and solid wastes, water pollution, hazardous substa
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