2015•Unpublished venueRequires access
Joint Distributions
Ramalingam Shanmugam, Rajan Chattamvelli
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Abstract
This chapter discusses the methodology to obtain the marginal, joint, and conditional probability distributions for both the discrete distributions and continuous distributions. Conditional distributions are obtained from joint distributions by conditioning on one or more variables. Conditional PDF's can be expressed in terms of joint PDF's using laws of conditional probabilities. The Jacobian determinant measures the stretching effect of a mapping or transformation. The Jacobian matrix contains the partial derivatives of the output variables with respect to the input variables in modeling problems that involve many input and output variables. The Jacobian determinant is a function of the variates when applied to variate transformations in statistics. The chapter discusses the most popular polar transformations that include: Plane Polar Transformations (PPT), Cylindrical Polar Transformations (CPT), and Spherical Polar Transformations (SPT).