actuar (version 3.3-4)

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, ...)
# S3 method for grouped.data
summary(object, ...)

Value

For quantile, a numeric vector, named if names is

TRUE.

For the summary method, an object of class

c("summaryDefault", "table") which has specialized

format and print methods.

Arguments

x, object

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.

Author

Vincent Goulet

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; mean.grouped.data and var.grouped.data to compute the mean and variance of grouped data.

grouped.data to create grouped data objects.

Examples

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