Cauchy Distribution

The Cauchy distribution is a probability distribution characterized by a peak around a central value but with very heavy tails, meaning extreme values are more likely than in distributions like the normal (bell curve). Unlike many distributions, its mean and variance are undefined, which makes typical averages unreliable. It’s often used to model situations with large, unpredictable fluctuations or noise. The distribution’s shape is symmetric and has a distinctive "bell" but with sluggish tails, indicating a higher chance of very extreme deviations, making it useful in fields like physics and signal processing where such behaviors occur.