WeibullFitter¶

class lifelines.fitters.weibull_fitter.WeibullFitter(*args, **kwargs)¶

This class implements a Weibull model for univariate data. The model has parameterized form:

\[S(t) = \exp\left(-\left(\frac{t}{\lambda}\right)^\rho\right), \lambda > 0, \rho > 0,\]

The \(\lambda\) (scale) parameter has an applicable interpretation: it represents the time when 63.2% of the population has died. The \(\rho\) (shape) parameter controls if the cumulative hazard (see below) is convex or concave, representing accelerating or decelerating hazards.

The cumulative hazard rate is

\[H(t) = \left(\frac{t}{\lambda}\right)^\rho,\]

and the hazard rate is:

\[h(t) = \frac{\rho}{\lambda}\left(\frac{t}{\lambda}\right)^{\rho-1}\]

After calling the .fit method, you have access to properties like: cumulative_hazard_, survival_function_, lambda_ and rho_. A summary of the fit is available with the method print_summary().

Parameters:: alpha (float, optional (default=0.05)) – the level in the confidence intervals.

Examples

from lifelines import WeibullFitter
from lifelines.datasets import load_waltons
waltons = load_waltons()
wbf = WeibullFitter()
wbf.fit(waltons['T'], waltons['E'])
wbf.plot()
print(wbf.lambda_)

cumulative_hazard_¶

The estimated cumulative hazard (with custom timeline if provided)

Type:: DataFrame

hazard_¶

The estimated hazard (with custom timeline if provided)

Type:: DataFrame

survival_function_¶

The estimated survival function (with custom timeline if provided)

Type:: DataFrame

cumulative_density_¶

The estimated cumulative density function (with custom timeline if provided)

Type:: DataFrame

density_¶

The estimated density function (PDF) (with custom timeline if provided)

Type:: DataFrame

variance_matrix_¶

The variance matrix of the coefficients

Type:: DataFrame

median_survival_time_¶

The median time to event

Type:: float

lambda_¶

The fitted parameter in the model

Type:: float

rho_¶

The fitted parameter in the model

Type:: float

durations¶

The durations provided

Type:: array

event_observed¶

The event_observed variable provided

Type:: array

timeline¶

The time line to use for plotting and indexing

Type:: array

entry¶

The entry array provided, or None

Type:: array or None

Notes

Looking for a 3-parameter Weibull model? See notes here.

lambda_: float¶

percentile(p) → float¶

Return the unique time point, t, such that S(t) = p.

Parameters:: p (float)

rho_: float¶