quantile.grouped.data {actuar}R Documentation

Quantiles of Grouped Data

Description

Sample quantiles corresponding to the given probabilities for objects of class "grouped.data".

Usage

## S3 method for class 'grouped.data'
quantile(x, probs = seq(0, 1, 0.25),
         names = TRUE, ...)

Arguments

x

an object of class "grouped.data".

probs

numeric vector of probabilities with values in [0, 1].

names

logical; if true, the result has a names attribute. Set to FALSE for speedup with many probs.

...

further arguments passed to or from other methods.

Details

The quantile function is the inverse of the ogive, that is a linear interpolation of the empirical quantile function.

The equation of the quantile function is

x = (c[j] (Fn(c[j-1]) - q) + c[j-1] (q - Fn(c[j])))/(Fn(c[j]) - Fn(c[j-1]))

for 0 <= q <= 1 and where c[0], …, c[r] are the r + 1 group boundaries and Fn is the empirical distribution function of the sample.

Value

A numeric vector, named if names is TRUE.

Author(s)

Vincent Goulet vincent.goulet@act.ulaval.ca

See Also

ogive for the smoothed empirical distribution of which quantile.grouped.data is an inverse; grouped.data to create grouped data objects.

Examples

data(gdental)
quantile(gdental)
Fn <- ogive(gdental)
Fn(quantile(gdental))		# inverse function

[Package actuar version 3.1-4 Index]