actuar (version 3.3-4)

ogive: Ogive for Grouped Data

Description

Compute a smoothed empirical distribution function for grouped data.

Usage

ogive(x, ...)
# S3 method for default
ogive(x, y = NULL, breaks = "Sturges", nclass = NULL, ...)
# S3 method for grouped.data
ogive(x, ...)
# S3 method for ogive
print(x, digits = getOption("digits") - 2, ...)
# S3 method for ogive
summary(object, ...)
# S3 method for ogive
knots(Fn, ...)
# S3 method for ogive
plot(x, main = NULL, xlab = "x", ylab = "F(x)", ...)

Value

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

"function" class.

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.

Author

Vincent Goulet and Mathieu Pigeon

Details

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

The equation of the ogive is $$G_n(x) = \frac{(c_j - x) F_n(c_{j - 1}) + (x - c_{j - 1}) F_n(c_j)}{c_j - c_{j - 1}}$$ for \(c_{j-1} < x \leq c_j\) and where \(c_0, \dots, c_r\) are the \(r + 1\) group boundaries and \(F_n\) is the empirical distribution function of the sample.

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)