R: Ogive for Grouped Data

ogive {actuar} | 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[0], …, 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.

### See Also

`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)

[Package actuar version 3.1-2 Index]