ogive: Ogive of the Expert Aggregated Distribution

In expert: Modeling without data using expert opinion

Description

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

Usage

ogive(x, ...)

## S3 method for class 'ogive'
print(x, digits = getOption("digits") - 2, ...)

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

## S3 method for class 'ogive'
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.

Details

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

The equation of the ogive is

G(x) = ((c[j] - x) F(c[j-1]) + (x - c[j-1]) F(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 and F is the cumulative distribution function.

Value

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

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)

Example output

Expert Aggregated Ogive
Call: ogive(fit)
    x = 3.05e+05, 5.1293e+05, 5.6342e+05, 6.2886e+05, 8.45e+05
 F(x) =      0,    0.1,    0.5,    0.9,      1
[1] 305000.0 512930.5 563423.2 628864.0 845000.0
[1] 0.0 0.1 0.5 0.9 1.0
[1] 0 0 0

expert documentation built on May 2, 2019, 2:27 p.m.