# ogive: Ogive for Grouped Data In actuar: Actuarial Functions and Heavy Tailed Distributions

 ogive R Documentation

## Ogive for Grouped Data

### Description

Compute a smoothed empirical distribution function for grouped data.

### Usage

```ogive(x, ...)

## Default S3 method:
ogive(x, y = NULL, breaks = "Sturges", nclass = NULL, ...)

## S3 method for class 'grouped.data'
ogive(x, ...)

## S3 method for class 'ogive'
print(x, digits = getOption("digits") - 2, ...)

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

## S3 method for class 'ogive'
knots(Fn, ...)

## S3 method for class 'ogive'
plot(x, main = NULL, xlab = "x", ylab = "F(x)", ...)
```

### Arguments

 `x` for the generic and all but the default method, an object of class `"grouped.data"`; for the default method, a vector of individual data if `y` is `NULL`, a vector of group boundaries otherwise. `y` a vector of group frequencies. `breaks, nclass` arguments passed to `grouped.data`; used only for individual data (when `y` is `NULL`). `digits` number of significant digits to use, see `print`. `Fn, object` an R object inheriting from `"ogive"`. `main` main title. `xlab, ylab` labels of x and y axis. `...` arguments to be passed to subsequent methods.

### Details

The ogive is a linear interpolation of the empirical cumulative distribution function.

The equation of the ogive is

Gn(x) = 1/(c[j] - c[j-1]) * [(c[j] - x) Fn(c[j-1]) + (x - c[j-1]) Fn(c[j])]

for c[j-1] < x <= c[j] and where c, …, c[r] are the r + 1 group boundaries and Fn is the empirical distribution function of the sample.

### Value

For `ogive`, a function of class `"ogive"`, inheriting from the `"function"` class.

### Author(s)

Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon

### References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (1998), Loss Models, From Data to Decisions, Wiley.

`grouped.data` to create grouped data objects; `quantile.grouped.data` for the inverse function; `approxfun`, which is used to compute the ogive; `stepfun` for related documentation (even though the ogive is not a step function).

### Examples

```## Most common usage: create ogive from grouped data object.
Fn <- ogive(gdental)
Fn
summary(Fn)
knots(Fn)                      # the group boundaries

Fn(knots(Fn))                  # true values of the empirical cdf
Fn(c(80, 200, 2000))           # linear interpolations

plot(Fn)                       # graphical representation

## Alternative 1: create ogive directly from individual data
## without first creating a grouped data object.
ogive(dental)                  # automatic class boundaries
ogive(dental, breaks = c(0, 50, 200, 500, 1500, 2000))

## Alternative 2: create ogive from set of group boundaries and
## group frequencies.
cj <- c(0, 25, 50, 100, 250, 500, 1000)
nj <- c(30, 31, 57, 42, 45, 10)
ogive(cj, nj)
```

actuar documentation built on July 16, 2022, 9:05 a.m.