Dataplot Vol 1 Vol 2

# EMPIRICAL CDF PLOT

Name:
EMPIRICAL CDF PLOT
Type:
Graphics Command
Purpose:
Generates a empirical cumulative distribution function (cdf) plot.
Description:
In reliability analysis, many data sets consists of a set of failure times, which may be truncated at some limit value. The cumulative distribution function (CDF) is defined as:

F(t) = prob(T < t)

where T is the lifetime of a randomly selected unit.

A empirical cdf plot is a plot of the empirical CDF versus failure time. The failure time is plotted on the horizontal axis. At each failure time, the following two points are calculated and plotted on the vertical axis:

$$y_1 = \frac{i-1}{n}$$
$$y_2 = \frac{i}{n}$$

with n and i denoting the number of data points and the rank of the failure time, respectively. The last failure time only calculates one of these points.

When all of the points are connected, a staircase type plot results. The vertical step is constant for the failure times, while the lengths of the horizontal steps are determined by the distances between failure times.

This plot is closely related to the TAIL AREA PLOT and the KAPLAN MEIER PLOT.

Syntax 1:
EMPIRICAL CDF PLOT <y>             <SUBSET/EXCEPT/FOR qualification>
where <y> is a response variable containing failure times;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
EMPIRICAL CDF PLOT <y> <x>             <SUBSET/EXCEPT/FOR qualification>
where <y> is a response variable containing counts;
<x> is a response variable containing failure times;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This synatx is used for binned data. That is, contains the failure times and contains the number of occurences corresponding to each failure time.

Examples:
EMPIRICAL CDF PLOT Y1
EMPIRICAL CDF PLOT Y1 SUBSET TAG > 1
EMPIRICAL CDF PLOT Y X
Default:
None
Synonyms:
None
Related Commands:
 LINES = Sets the type for plot lines. CHARACTERS = Sets the type for plot characters. TAIL AREA PLOT = Generates a tail area plot. KAPLAN MEIER PLOT = Generates a Kaplan Meier plot. ... HAZARD PLOT = Generates a hazard plot. PROBABILITY PLOT = Generates a probability plot. PLOT = Generates a data or function plot.
Applications:
Reliability
Implementation Date:
1998/8
Program:
SKIP 25