Table of contents
The density function of the Cauchy distribution:
f(x; \mu, \sigma) = \dfrac{1}{\pi \sigma \left[ 1 + \left( \frac{x - \mu}{\sigma} \right)^2 \right]}
Methods for scalar input, as well as for list input, are listed below.
.. autofunction:: pystats.dcauchy(x: float, mu: float = 0.0, sigma: float = 1.0, log: bool = False) -> float :noindex:
.. autofunction:: pystats.dcauchy(x: List[float], mu: float = 0.0, sigma: float = 1.0, log: bool = False) -> List[float] :noindex:
The cumulative distribution function (CDF) of the Cauchy distribution:
F(x; \mu, \sigma) = \int_{-\infty}^x f(z; \mu, \sigma) dz = 0.5 + \dfrac{1}{\pi} \text{arctan}\left( \frac{x - \mu}{\sigma} \right)
Methods for scalar input, as well as for list input, are listed below.
.. autofunction:: pystats.pcauchy(p: float, mu: float = 0.0, sigma: float = 1.0, log: bool = False) -> float :noindex:
.. autofunction:: pystats.pcauchy(p: List[float], mu: float = 0.0, sigma: float = 1.0, log: bool = False) -> List[float] :noindex:
The quantile function of the Cauchy distribution:
q(p; \mu, \sigma) = \mu + \gamma \text{tan} \left( \pi (p - 0.5) \right)
Methods for scalar input, as well as for list input, are listed below.
.. autofunction:: pystats.qcauchy(q: float, mu: float = 0.0, sigma: float = 1.0) -> float :noindex:
.. autofunction:: pystats.qcauchy(q: List[float], mu: float = 0.0, sigma: float = 1.0) -> List[float] :noindex:
Random sampling for the Cauchy distribution is achieved via the inverse probability integral transform.
.. autofunction:: pystats.rcauchy(mu: float = 0.0, sigma: float = 1.0) -> float :noindex:
.. autofunction:: pystats.rcauchy(n: int, mu: float = 0.0, sigma: float = 1.0) -> List[float] :noindex: