# quantile.grouped.data: Quantiles of Grouped Data In actuar: Actuarial Functions and Heavy Tailed Distributions

 quantile.grouped.data 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, ...)

## 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 vincent.goulet@act.ulaval.ca

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.