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Approximating the Cumulative Distribution Function of Bivariate Truncated Normal Distribution

This document presents an approach to approximating the cumulative distribution function (CDF) for the bivariate left-truncated normal distribution. Authored by Arvid C. Johnson and Binod K. Dhungel at Dominican University, it details the relevant probability density functions (PDF) and cumulative distribution functions using standardized forms. The text examines inner and edge cell behaviors, and includes tables of approximated values for varying parameters, such as correlation and truncation levels. Additionally, it provides a downloadable Excel function for practical application.

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Approximating the Cumulative Distribution Function of Bivariate Truncated Normal Distribution

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  1. Approximation of the Cumulative Distribution Function of the Bivariate Truncated Normal Distribution Arvid C. Johnson and Binod K. Dhungel Dominican University River Forest, Illinois

  2. Probability Density Function Cumulative Distribution Function Notational Conventions – Bivariate Normal

  3. Probability Density Function Cumulative Distribution Function Notational Conventions – Standardized Form

  4. What is the Bivariate (Left-)Truncated Normal?

  5. The Probability Density Function The Cumulative Distribution Function Bivariate Left Truncated Normal

  6. Standardized Form of BLTN… The Probability Density Function The Cumulative Distribution Function

  7. At inner Cells Approach modified at edges. Approximation Method for Average Volume

  8. The Cumulative Distribution Function of Standard Bivariate Left Truncated Normal

  9. Table 1 – FSBLTN(z1,z2) for kL1 = -2, kL2 = -1, and  = -0.3 FSBLTN for z1= -2(0.5)4 and z2 = -1(0.2)4

  10. Table 2 – FSBLTN(z1,z2) where z1 = z2 for kL1 = -2, kL2 = -1 and  = -0.9(0.2)0.9 (and  = 0). FSBLTN for z1= z2 = –1(0.2)4

  11. “TruncatedBivariateNormal.xls” is available for download…  The Excel Function

  12. Thank You! http://domin.dom.edu/faculty/ajohnson/bivartruncnorm.htm ajohnson@dom.edu

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