R: Quantiles of Grouped Data

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 3.1-2 Index]