burr12_sf

mdtools.functions.burr12_sf(t, tau=1, beta=1, delta=1)[source]

Survival function of the Burr Type XII distribution function:

\[S(t) = \frac{ 1 }{ \left[ 1 + \left( \frac{t}{\tau} \right)^\beta \right]^\delta }\]

For \(\beta = 1\), the Burr Type XII distribution becomes the Lomax distribution and for \(\delta = 1\) it becomes the log-logistic distribution. The survival function of the Lomax distribution is equal to the Becquerel decay law.

Parameters:

t (scalar or array_like) – Value(s) at which to evaluate \(f(t)\).
tau (scalar or array_like, optional) – Scale parameter(s).
beta (scalar or array_like, optional) – Shape parameter(s).
delta (scalar or array_like, optional) – Shape parameter(s).

Returns:

sf (scalar or numpy.ndarray) – The outcome of \(S(t)\). \(S(t)\) is evaluated element-wise if at least one of the input arguments is an array.