Non Parametric models
Non Parametric models offer a straightforward and easytointerpret way to compute the survival and hazard functions without imposing any assumptions. Pysurvival provides the following nonparametric models:
 KaplanMeier model (
KaplanMeierModel
)  Smooth KaplanMeier model (
SmoothKaplanMeierModel
)
KaplanMeier model
One of the most straightforward ways to estimate the Survival function of an entire group, is by using the KaplanMeier method. Given units in a cohort, let's assume that there are distinct actual event times such that with , then the Survival function estimator is given by: with:
 is the number of individuals experiencing an event at
 is the number of individuals at risk within  those who have not been censored or experienced an event
Smooth KaplanMeier
Despite its ease of use, the main drawback of the KaplanMeier estimator is that it is a step function with jumps. Kernel smoothing can therefore solve this issue, provided that the best kernel and bandwidth are properly chosen.
Let be a Smooth estimator of the KaplanMeier survival function. can be written such that:
with:
 , the height of the jump of the KaplanMeier estimator at

, the infinite order kernel function. Here are the most common kernel functions:
Biweight
: if elseCosine
: if elseEpanechnikov
: if elseNormal
:Triweight
: if elseUniform
: if else

, the kernel function bandwidth
References
 https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator
 Kaplan, E. L.; Meier, P. (1958). "Nonparametric estimation from incomplete observations". J. Amer. Statist. Assoc. 53 (282): 457–481. doi:10.2307/2281868. JSTOR 2281868.
 https://www.researchgate.net/publication/50940632_Understanding_survival_analysis_KaplanMeier_estimate
 survPresmooth: An R Package for PreSmooth Estimation in Survival Analysis
 Nonparametric density estimation from censored data
 CDF and survival function estimation with infiniteorder kernels