Statistics: ecdf

### Function Reference: `ecdf`

statistics: [f, x] = ecdf (y)
statistics: [f, x, flo, fup] = ecdf (y)
statistics: ecdf (…)
statistics: ecdf (ax, …)
statistics: […] = ecdf (y, name, value, …)
statistics: […] = ecdf (ax, y, name, value, …)

Empirical (Kaplan-Meier) cumulative distribution function.

`[f, x] = ecdf (y)` calculates the Kaplan-Meier estimate of the cumulative distribution function (cdf), also known as the empirical cdf. y is a vector of data values. f is a vector of values of the empirical cdf evaluated at x.

`[f, x, flo, fup] = ecdf (y)` also returns lower and upper confidence bounds for the cdf. These bounds are calculated using Greenwood’s formula, and are not simultaneous confidence bounds.

`ecdf (…)` without output arguments produces a plot of the empirical cdf.

`ecdf (ax, …)` plots into existing axes ax.

`[…] = ecdf (y, name, value, …)` specifies additional parameter name/value pairs chosen from the following:

name | value
--- | ---
"censoring" | A boolean vector of the same size as Y that is 1 for observations that are right-censored and 0 for observations that are observed exactly. Default is all observations observed exactly.
"frequency" | A vector of the same size as Y containing non-negative integer counts. The jth element of this vector gives the number of times the jth element of Y was observed. Default is 1 observation per Y element.
"alpha" | A value alpha between 0 and 1 specifying the significance level. Default is 0.05 for 5% significance.
"function" | The type of function returned as the F output argument, chosen from "cdf" (the default), "survivor", or "cumulative hazard".
"bounds" | Either "on" to include bounds or "off" (the default) to omit them. Used only for plotting.

Type `demo ecdf` to see examples of usage.

See also: cdfplot, ecdfhist

Source Code: ecdf

### Example: 1

     y = exprnd (10, 50, 1);    ## random failure times are exponential(10)
     d = exprnd (20, 50, 1);    ## drop-out times are exponential(20)
     t = min (y, d);            ## we observe the minimum of these times
     censored = (y > d);        ## we also observe whether the subject failed

     ## Calculate and plot the empirical cdf and confidence bounds
     [f, x, flo, fup] = ecdf (t, "censoring", censored);
     stairs (x, f);
     hold on;
     stairs (x, flo, "r:"); stairs (x, fup, "r:");

     ## Superimpose a plot of the known true cdf
     xx = 0:.1:max (t); yy = 1 - exp (-xx / 10); plot (xx, yy, "g-");
     hold off;

### Example: 2

     R = wblrnd (100, 2, 100, 1);
     ecdf (R, "Function", "survivor", "Alpha", 0.01, "Bounds", "on");
     hold on
     x = 1:1:250;
     wblsurv = 1 - cdf ("weibull", x, 100, 2);
     plot (x, wblsurv, "g-", "LineWidth", 2)
     legend ("Empirical survivor function", "Lower confidence bound", ...
             "Upper confidence bound", "Weibull survivor function", ...
             "Location", "northeast");
     hold off