Definition 1: The Cauchy distribution is the non-standard t distribution, T(1, µ, σ), with degrees of freedom ν = 1. This means that the pdf takes the form
The cdf takes the form
The Cauchy distribution is similar to the normal distribution except that it has much thicker tails. It is unusual in that the mean, variance, skewness, and kurtosis are all undefined. The mode and median are equal to µ and the distribution is symmetric around x = µ.
The Real Statistics formula that calculates the cdf and pdf of the Cauchy distribution is T3_DIST(x, 1, μ, σ, cum) and the formula that calculates the inverse function is T3_INV(p, 1, μ, σ).
Reference
Wikipedia (2020) Cauchy distribution
https://en.wikipedia.org/wiki/Cauchy_distribution