Cauchy distribution
Topic of Simulation, part of Probability
Cauchy distribution
| Type | Topic |
| Taught in | Simulation |
| Part | Probability |
The law with density 1/\{\pi(1+x^2)\} on the real line. It has no mean, so averages of Cauchy draws never settle down, and the law of large numbers does not apply. Its distribution function \tfrac12+\arctan(x)/\pi inverts in closed form, so it is easy to simulate.
In Simulation
From Simulation
The method needs a usable inverse. The exponential, uniform, Weibull, logistic and Cauchy distribution functions invert in closed form. Many others do not, and even a closed inverse can be a poor algorithm if it is expensive to evaluate.
Used in
- Taught in Simulation
- All 4 questions on Simulation
See also
Law of large numbers · Cumulative distribution function · Linear congruential generator · Inverse-transform method · Acceptance–rejection method · Random numbers · Draws from the usual families · Box–Muller method