knitr::opts_chunk$set( collapse = TRUE, comment = "#>", fig.dim = c(7, 4) ) library(wurmc) options(width = 100, digits = 2)
The statgenGWAS package has been designed for performing single trait Genome Wide Association Studies (GWAS).
gData
The computation of the Nth Fibonacci number in this function uses the formula obtained from solving the recurrence relation $$F_{n} = F_{n-1} + F_{n-2},$$ which translates to the equation, $x^{n} = x^{n-1} + x^{n-2}$, and then to $x^2 = x + 1$. The two solutions to the latter equation are $\phi$ and $\psi$, where $$\phi=\frac{1+\sqrt{5}}{2}, \qquad \psi=\frac{1-\sqrt{5}}{2}.$$
This eventually leads to the formula used in this function, $$F_{n} =\frac{\phi^{n} - \psi^{n}}{\sqrt{5}}.$$
$$\sigma = \sqrt{\frac{Z}{n} \sum \textstyle \frac{1}{2} \displaystyle \left[ \left( \log \frac{H_i}{L_i}\right)^2 - \left(2 \log 2 - 1 \right) \left( \log \frac{C_i}{O_i}\right)^2 \right]}$$
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