expert (version 1.0-0)

ogive: Ogive of the Expert Aggregated Distribution

Description

Compute a smoothed empirical distribution function for objects of class "expert".

Usage

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

Arguments

x

an object of class "expert"; for the methods, an object of class "ogive", typically.

digits

number of significant digits to use, see print.

Fn

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 $$G(x) = \frac{(c_j - x) F(c_{j - 1}) + (x - c_{j - 1}) F(c_j)}{c_j - c_{j - 1}}$$ 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

expert to create objects of class "expert"; cdf for the true cumulative distribution function; approxfun, which is used to compute the ogive; stepfun for related documentation (even though the ogive is not a step function).

Examples

x <- list(E1 <- list(A1 <- c(0.14, 0.22, 0.28),
                     A2 <- c(130000, 150000, 200000),
                     X <- c(350000, 400000, 525000)),
          E2 <- list(A1 <- c(0.2, 0.3, 0.4),
                     A2 <- c(165000, 205000, 250000),
                     X <- c(550000, 600000, 650000)),
          E3 <- list(A1 <- c(0.2, 0.4, 0.52),
                     A2 <- c(200000, 400000, 500000),
                     X <- c(625000, 700000, 800000)))
probs <- c(0.1, 0.5, 0.9)
true.seed <- c(0.27, 210000)
fit <- expert(x, "cooke", probs, true.seed, 0.03)
Fn <- ogive(fit)
Fn
knots(Fn)            # the group boundaries

Fn(knots(Fn))        # true values of the empirical cdf
Fn(c(80, 200, 2000)) # linear interpolations

plot(Fn)