GeneralizedGammaFitter¶

class lifelines.fitters.generalized_gamma_fitter.GeneralizedGammaFitter(*args, **kwargs)¶

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

The survival function is:

\[\begin{split}S(t)=\left\{ \begin{array}{} 1-\Gamma_{RL}\left( \frac{1}{{{\lambda }^{2}}};\frac{{e}^{\lambda \left( \frac{\log(t)-\mu }{\sigma} \right)}}{\lambda ^{2}} \right) \textit{ if } \lambda> 0 \\ \Gamma_{RL}\left( \frac{1}{{{\lambda }^{2}}};\frac{{e}^{\lambda \left( \frac{\log(t)-\mu }{\sigma} \right)}}{\lambda ^{2}} \right) \textit{ if } \lambda \le 0 \\ \end{array} \right.\,\!\end{split}\]

where \(\Gamma_{RL}\) is the regularized lower incomplete Gamma function.

This model has the Exponential, Weibull, Gamma and Log-Normal as sub-models, and thus can be used as a way to test which model to use:

When \(\lambda = 1\) and \(\sigma = 1\), then the data is Exponential.
When \(\lambda = 1\) then the data is Weibull.
When \(\sigma = \lambda\) then the data is Gamma.
When \(\lambda = 0\) then the data is Log-Normal.
When \(\lambda = -1\) then the data is Inverse-Weibull.
When \(\sigma = -\lambda\) then the data is Inverse-Gamma.

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

Important

The parameterization implemented has \(\log\sigma\), thus there is a ln_sigma_ in the output. Exponentiate this parameter to recover \(\sigma\).

Important

This model is experimental. It’s API may change in the future. Also, it’s convergence is not very stable.

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

Examples

from lifelines import GeneralizedGammaFitter
from lifelines.datasets import load_waltons
waltons = load_waltons()

ggf = GeneralizedGammaFitter()
ggf.fit(waltons['T'], waltons['E'])
ggf.plot()
ggf.summary

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

alpha_¶

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

percentile(p)¶

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

Parameters:: p (float)