quantile.grouped.data: Quantiles of Grouped Data

In actuar: Actuarial Functions and Heavy Tailed Distributions

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, ...)

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

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.

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.

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.

Author(s)

Vincent Goulet [e-mail]

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

actuar documentation built on Nov. 8, 2023, 9:06 a.m.