actuar (version 1.2-2)

ogive: Ogive for Grouped Data

Description

Compute a smoothed empirical distribution function for grouped data.

Usage

ogive(x, y = NULL)
"print"(x, digits = getOption("digits") - 2, ...)
"summary"(object, ...)
"knots"(Fn, ...)
"plot"(x, main = NULL, xlab = "x", ylab = "F(x)", ...)

Arguments

x

an object of class "grouped.data" or a vector of group boundaries in ogive; for the methods, an object of class "ogive", typically.

y

a vector of group frequencies; used only if x does not inherit from class "grouped.data".

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.

Value

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

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

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

data(gdental)
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)