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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.
You and your team have been hired as strategic consultants by the hugely successful retailer known as “Cutie Pie”. The company sells many products, although one product in particul
In the experimental studies, the collection of individuals to which the experimental process of interest is not applied. In the observational studies, most often used for a collect
A term usually used for unobserved individual heterogeneity. Such variation is of main concern in the medical statistics particularly in the analysis of the survival times where ha
Your first task is to realize two additional data generation functions. Firstly, extend the system to generate random integral numbers based on normal distribution. You need to stu
The plot of the number of cases of the disease against the time period. A large and sudden increase corresponds to an epidemic. The example of this is shown in the figure drawn bel
A mixture of benzene, toluene, and xylene enters a two-stage distillation process where some of the componentsare recovered. The distillation process operates at steady-state condi
Chebyshev's inequality: A statement about the proportion of the observations which fall within some number of the standard deviations of the mean for any of the probability distri
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
Normal approximation : Normal distributions which approximate other distributions; such as, a normal distribution with the mean np and variance np(1 - p) which acts as an approxima
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
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