# 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 = (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, …, c[r] are the r + 1 group boundaries and Fn 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 July 16, 2022, 9:05 a.m.