The Lorenzian Function Formula
The Lorenzian function, also known as the Cauchy distribution, is a probability distribution that describes certain physical phenomena, particularly resonance phenomena in physics. The Lorenzian function has the following formula: L(x; x_0, γ) = γ / [(x − x_0)² + γ²] where: x is the independent variable x_0 is the peak position parameter γ is the line width parameter, also called the half-width at half-maximum (HWHM) The formula describes a bell-shaped curve with a peak at x_0 and a width determined by γ. It has a slower decay than the Gaussian distribution, and its tails extend to infinity in both directions. The Cauchy distribution has no finite moments, which means that the mean and variance are undefined. The Lorenzian function formula is a mathematical formula that is used in trading to model price movements of financial instruments. It is particularly useful in options trading because it can provide an estimate of the probability distribution of future price movements...