actuar (version 3.0-0)

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 \(0 \leq q \leq c_j\) 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
# }