ecdf
Empirical Cumulative Distribution Function
Description
Create and use an empirical cumulative distribution function for a given sample.
Usage
ecdf(x)
## S3 method for class 'ecdf':
print(x, digits = getOption("digits") - 2, ...)
## S3 method for class 'ecdf':
summary(object, ...)
## S3 method for class 'ecdf':
quantile(x, ...)
Arguments
| x, object |
a numeric vector of variable data for ecdf function (which
will drop any NA values in it), or an ecdf object
for the summary and quantile methods.
|
| digits |
the number of significant digits that should be printed.
|
| ... |
The quantile method passes on all other arguments to the default
quantile method.
The summary and print methods ignore all the other arguments.
|
Details
The empirical cumulative distribution function(or ecdf), is the cumulative
distribution function associated with the empirical measure of the sample.
It is a step function that jumps up by 1/n at each of the n data points.
Lets x = (x1, ..., xn) be real random variables with the common cumulative
distribution function F(t). Then the empirical cumulative distribution function
is defined as:
Fn(t) = {xi<=t}/n = (1/n)*sum(indicator{xi<=t}), where i = 1, 2, ..., n.
print.ecdf is an invisible method of print for the object
of class "ecdf". It prints out the "call" attribute and and the first few
and list of the knots.
summary.ecdf is an invisible method of summary for the
object of class "ecdf". It returns the summary of the knots of the "ecdf" object,
ignoring their counts.
quantile.ecdf is an invisible method of quantile for the
object of class "ecdf". The quantiles it computes match those of the
original data.
Value
ecdf(x) returns a function that may be called to evaluate the empirical
distribution function of x at any desired values.
The returned function has class c("ecdf", "stepfun", "function") and
with attribute "call"(matched call). There are also some objects in the
environment of this function: "f", "method", "n", "nobs", "x", "y", "yleft"
and "yright". All of them are returned by function approxfun internally,
except for "nobs", which is the number of original data by skipping NAs.
print.ecdf returns the input "ecdf" object itself invisibly.
summary.ecdf returns the summary of knots of the input "ecdf" object
with attribute "header" and class name "summary.ecdf".
quantile.ecdf returns a vector of the quantiles of the original data.
plot.ecdf returns NULL, invisibly. It does nothing except
warn the user that it is not implemented.
References
Shorack, G.R. and Wellner, J.A. 1986. Empirical processes with applications to statistics. New York, NY: John Wiley & Sons.
van der Vaart, A.W. 1998. Asymptotic Statistics. Cambridge, UK: Cambridge University Press.
See Also
Examples
e <- ecdf(Sdatasets::fuel.frame$Mileage)
e(c(20, 30, 40)) # proportion of Mileage values at or below 20, 30, and 40
quantile(e)
quantile(Sdatasets::fuel.frame$Mileage) # same as previous
summary(e) # shows quantiles of unique values of Mileage