Create a survival distribution from some right-censored survival data:

Visualize the survival function:

Compute moments and quantiles:

Compare the survival rates of breast cancer patients with different immuno-histochemical responses, given the following data and that follow-up times were 116 and 87 weeks for groups one and two, respectively:

Estimate the distributions of each group:

Visually compare the survival functions:

Find the average number of weeks a breast cancer patient survives in the two groups:

Ignoring censoring causes an underestimate in the survival function:

A group of 191 high-school boys was asked the exact age at which they started using marijuana. Responses were "I used it first at age ", "I never used it", and "I have used it but cannot recall when the first time was". Estimate the survival function for time to first marijuana use given the following data:

The probability of a person not having used marijuana at a certain age:

Find the probability of a person having used marijuana at age 15 or earlier:

Estimate the survival of children with acute leukemia treated with the drug 6-mercaptopurine using the Nelson–Aalen and Kaplan–Meier estimators:

The estimates are quite similar:

Plot the Nelson–Aalen estimate of the cumulative hazard function:

Compare survival curves for patients with acute myelogenous leukemia given extended maintenance of chemotherapy (M) versus non-maintained (NM) chemotherapy using the following data:

Show markers at the occurrence of censored observations:

It appears that survival is longer when chemotherapy is maintained:

Estimate the cumulative hazard function for time to retraction for breast cancer patients treated by radiotherapy given the following data:

Show the resulting cumulative hazard function:

Compute the expected time to retraction given the absence of retraction by week 20:

A set of manufactured cords was placed under stress until breakage. Some of the cords were damaged in some way during the study and so their true reliability is right censored. Given the data, estimate the reliability function:

The reliability function is the probability a cord will hold beyond a particular stress:

Determine the expected breaking point, given a cord has not broken at 45 lbs of stress:

The break-point data for 17 ropes is given where the maximum stress applied was 100 lbs of force. Compare the empirical estimate to a Weibull model:

Model the survival function with a censored Weibull distribution:

An empirical model using SurvivalDistribution:

Compute the probability a rope will break beyond 60 lbs of force using the two models:

Probabilities for each observation are distributed in the direction of censoring:

The impact of adding three observations each for three censoring types:

Right-censored observations are truncated at the largest finite endpoint:

The estimates are equivalent:

If the last observation is right censored, the distribution is truncated:

The survival function is truncated at the last finite endpoint at 25:

This endpoint can be set arbitrarily, using a list of weights:

The value 30 was added to the domain of the distribution without adding any observations:

Agreement with the uncensored case diverges with an increased proportion of censoring:

The PDF and hazard function are discrete:

For comparison to continuous distributions, the cumulative hazard function can be used:

CensoredDistribution applies censoring to a distribution, not individual observations:

Treat all observations outside of the window as right censored:

Using Clip on data is equivalent to CensoredDistribution over the same window:

The estimates are equivalent:

With no censoring, SurvivalDistribution is equivalent to EmpiricalDistribution:

Using SurvivalDistribution with TruncatedDistribution is not equivalent to applying truncation to the data if censoring is present:

In the absence of censoring, these are equivalent: