KaplanMeierECDF Class |
Namespace: Imsl.Stat
The KaplanMeierECDF type exposes the following members.
Name | Description | |
---|---|---|
KaplanMeierECDF | Constructor for KaplanMeierECDF.
|
Name | Description | |
---|---|---|
Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
EvaluateCDF | Computes the empirical CDF and returns the CDF values up to, but not
including the time values returned by GetTimes.
| |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |
GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetTimes | Retrieves the time values where the step function CDF jumps to a greater
value.
| |
GetType | Gets the Type of the current instance. (Inherited from Object.) | |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
SetCensor | Set flags to note right-censoring.
| |
SetFrequency | Sets the frequency for each entry in t.
| |
ToString | Returns a string that represents the current object. (Inherited from Object.) |
Name | Description | |
---|---|---|
NumberOfPoints |
The number of points in the empirical CDF.
|
The Kaplan-Meier (K-M) Product Limit procedure provides simple estimates of the reliability function or the CDF based on failure data that may be multi-censored. No underlying probability model is assumed; K-M estimation is an empirical (non-parametric) procedure. Exact times of failure are required.
Consider a situation in which we are reliability testing n (non-repairable) units taken randomly from a population. We are investigating the population to determine if its failure rate is acceptable. In the typical test scenario, we have a fixed time T to run the units to see if they survive or fail. The data obtained are called Censored Type I data.
During the T hours of test we observe r failures (where r can be any number from 0 to n). The failure times are , and there are units that survived the entire T-hour test without failing. Note that T is fixed in advance, and r is an output of the testing, since we don't know how many failures will occur until the test is run. Note that we assume the exact times of failure are recorded when they occur.
This type of data is also called "right censored" data since the times of failure to the right (i.e., larger than T) are missing. The steps for calculating K-M estimates are the following:
Note that non-failed units taken off testing (i.e., right-censored) only count up to the last actual failure time before they were removed. They are included in the counts up to and including that failure time, but not after.