ogive {actuar}R Documentation

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, ...)

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

## S3 method for class 'ogive':
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.

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

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

for c[j-1] < x <= c[j] and where c[0], ..., c[r] are the r + 1 group boundaries.

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; 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)

[Package actuar version 0.9-7 Index]