actuar (version 0.9-3)

ogive: Ogive for grouped data

Description

Compute a smoothed empirical distribution function for grouped data.

Usage

ogive(x, y = NULL, ...)
## S3 method for class 'ogive':
print(x, digits = getOption("digits") - 2, ...)
## S3 method for class 'ogive':
summary(object, \dots)
## S3 method for class 'ogive':
knots(Fn, \dots)
## S3 method for class 'ogive':
plot(x, \dots, 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 Robject 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 of a grouped data set links the values of the empirical cumulative distribution known at group boundaries by straight line segments, resulting in an approximation of the empirical cdf. The equation of the ogive is $$F_n(x) = \frac{(c_j - x) F_n(c_{j-1}) + (x - c_{j-1}) F_n(c_j)}{c_j - c_{j - 1}}$$ for $c_{j-1} < x \leq c_j$ and where $c_0, \dots, c_r$ are the $r + 1$ group boundaries.

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; 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)