actuar (version 2.3-3)

quantile.grouped.data: Quantiles of Grouped Data

Description

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

Usage

# S3 method for 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.

Value

A numeric vector, named if names is TRUE.

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 $$x=\frac{c_j(F_n(c_{j-1})-q)+c_{j-1}(q-F_n(c_j)}{F_n(c_j)-F_n(c_{j-1})}$$ for $0\le q\le c_j$ and where $c_0,\dots ,c_r$ are the $r+1$ group boundaries and $F_n$ is the empirical distribution function of the sample.

See Also

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

Examples

# NOT RUN {
data(gdental)
quantile(gdental)
Fn <- ogive(gdental)
Fn(quantile(gdental))		# inverse function
# }