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The equation is a simplified bivariate form of Cholesky decomposition. This simplified equation is sometimes called the Kaiser-Dickman algorithm (Kaiser & Dickman, 1962).

Note that $X_1$ and $X_2$ must be normal variables with the same variance for this algorithm to work properly.

References:

Kaiser, H. F., & Dickman, K. (1962). Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika, 27(2), 179-182.

The equation is a simplified bivariate form of Cholesky decomposition. This simplified equation is sometimes called the Kaiser-Dickman algorithm (Kaiser & Dickman, 1962).

Note that $X_1$ and $X_2$ must have the same variance for this algorithm to work properly. Also, the algorithm is typically used with normal variables. If $X_1$ or $X_2$ are not normal, $Y$ might not have the same distributional form as $X_2$.

References:

Kaiser, H. F., & Dickman, K. (1962). Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika, 27(2), 179-182.

The equation is a simplified bivariate form of Cholesky decomposition. This simplified equation is sometimes called the Kaiser-Dickman algorithm (Kaiser & Dickman, 1962).

Note that $X_1$ and $X_2$ must be standard normal variables for this algorithm to work properly.

References:

Kaiser, H. F., & Dickman, K. (1962). Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika, 27(2), 179-182.

The equation is a simplified bivariate form of Cholesky decomposition. This simplified equation is sometimes called the Kaiser-Dickman algorithm (Kaiser & Dickman, 1962).

Note that $X_1$ and $X_2$ must be normal variables with the same variance for this algorithm to work properly.

References:

Kaiser, H. F., & Dickman, K. (1962). Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika, 27(2), 179-182.

The equation is a simplified bivariate form of Cholesky decomposition. This simplified equation is sometimes called the Kaiser-Dickman algorithm (Kaiser & Dickman, 1962).

Note that $X_1$ and $X_2$ must be standard normal variables for this this algorithm to work properly.

References:

Kaiser, H. F., & Dickman, K. (1962). Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika, 27(2), 179-182.

The equation is a simplified bivariate form of Cholesky decomposition. This simplified equation is sometimes called the Kaiser-Dickman algorithm (Kaiser & Dickman, 1962).

Note that $X_1$ and $X_2$ must be standard normal variables for this algorithm to work properly.

References:

Kaiser, H. F., & Dickman, K. (1962). Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika, 27(2), 179-182.