Create an empirical model for some right-censored survival data:

Use like any other distribution:

Compute probabilities and expectations:

Create a nonparametric maximum likelihood estimate for doubly censored data:

Use

Censoring to convert status indicators:

Visualize the survival and cumulative hazard functions:

Estimate the distribution for interval-censored data:

The empirical distribution function:

Sample from the distribution:

Specify weights to easily input frequency data:

These weights indicate double censoring:

The estimated survival function:

Estimate distribution functions:

The PDF and hazard function are discrete:

The CDF and survival function are piecewise constant:

Compute moments of the distribution:

Special moments:

General moments:

Quantile function:

Special quantile values:

Generate random numbers:

Only values in the distribution domain are possible:

Compute probabilities and expectations:

Uncensored data can be represented on intervals

(no censoring):

The survival functions are equivalent:

Estimate the distribution with right-censored data (right censoring):

The jump at 16 has been removed and the survival function has been rescaled beyond 16:

A single left-censored observation (left censoring):

The jump at 16 is removed and the probability is redistributed over the estimate:

Observations can be censored on an interval (interval censoring):

The third observation occurred somewhere on the interval

:

Any combination of left- and right-censored observations is possible (double censoring):

The second observation is left censored and the fourth is right censored:

Any type of censoring can be present in the data simultaneously (mixed censoring):

The second, third, and fourth observations are left, interval, and right censored respectively:

Use

Censoring with status indicators to indicate censored observations:

Create distributions for the different censoring schemes:

The survival functions:

Provide a list of observation weights:

The second value was observed twice, causing a greater decline in the survival function at 15:

Setting the weight argument to

Automatic is equivalent to using constant weights:

The estimates are equivalent:

Specify right censoring with a list of weights:

There was one right-censored observation at 15:

Left-censored observations can also be specified in a list of weights:

There were three left-censored observations at 15:

Uncensored, right-censored, and left-censored observations can be specified simultaneously:

There were two uncensored, one right-censored, and three left-censored observations at 15:

The weight list can be used with interval-censored observations:

The second observation is interval censored and occurred twice:

The weight list can be used to drop unwanted observations:

The second observation was dropped: