Non-Normal Bivariate Distributions with Normal Marginals

Examples of non-normal bivariate (multivariate) distributions with normal marginals [15, 16, 18] can be used in the classroom to (a) contrast the correlation/ regression structures of these distributions with that of the corresponding bivariate normal model [9, 10, 11, 12], (b) investigate the feasibility of employing coordinate transformations to normality as a prelude to analyses based on the assumption of joint normality [2, 13, 15, 16, 17, 18, 27] and (c) motivate the need for the development of multidimensional goodness-of-fit tests [2, 13, 16]. In addition, since most of the examples presented here are concerned with ways to generate distributions with arbitrary marginals, they can also be used to obtain a wide variety of non-normal bivariate (multivariate) distributions for these, and other, purposes [2, 11, 12, 13].

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