Bivariate Normal

Nick T. Thomopoulos
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Nick T. Thomopoulos: Illinois Institute of Technology, Stuart School of Business

Chapter Chapter 19 in Statistical Distributions, 2017, pp 153-163 from Springer

Abstract: Abstract Over the years a great many scholars have contributed to the literature concerning the bivariate normal distribution. In 1998, Montira Jantaravareerat and N. Thomopoulos describe a way to estimate the cumulative probability of the distribution. In this chapter, a new method is shown on computing the joint cumulative probability. The bivariate normal has two variables, x1, x2, that are jointly related, and has five parameters, μ1, μ2, σ1, σ2, ρ. The marginal distributions are normally distributed, and when the value of one of the variables is known, the distribution on the other is also normally distributed. The variables are converted to a new set, z1, z2, that are jointly related by the bivariate standard normal distribution. The latter two variables are easier to apply mathematically in the computations. An approximation method is developed here to compute the joint probability of the two variables. Table values are listed and examples are presented to demonstrate the application.

Keywords: Bivariate Standard Normal Distribution; Joint Cumulative Probability; Relative Joint; Marginal Distribution; Table Values (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-65112-5_19

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DOI: 10.1007/978-3-319-65112-5_19

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