When simpver = NULL, the explicit Preston equation is selected:
$$ y = b\ \sqrt{1-\left(\frac{x}{a}\right)^2}\left(1+c_{1}\ \frac{x}{a}+c_{2}\left(\frac{x}{a}\right)^2+c_{3}\left(\frac{x}{a}\right)^3\right), $$
where P has five parameters: \(a\), \(b\), \(c_{1}\), \(c_{2}\), and \(c_{3}\).
\(\quad\) When simpver = 1, the simplified version 1 is selected:
$$ y = b\ \sqrt{1-\left(\frac{x}{a}\right)^2}\left(1+c_{1}\ \frac{x}{a}+c_{2}\left(\frac{x}{a}\right)^2\right), $$
where P has four parameters: \(a\), \(b\), \(c_{1}\), and \(c_{2}\).
\(\quad\) When simpver = 2, the simplified version 2 is selected:
$$ y = b\ \sqrt{1-\left(\frac{x}{a}\right)^2}\left(1+c_{1}\ \frac{x}{a}\right), $$
where P has three parameters: \(a\), \(b\), and \(c_{1}\).
\(\quad\) When simpver = 3, the simplified version 3 is selected:
$$ y = b\ \sqrt{1-\left(\frac{x}{a}\right)^2}\left(1+c_{2}\left(\frac{x}{a}\right)^2\right), $$
where P has three parameters: \(a\), \(b\), and \(c_{2}\).