ogive {expert} | R Documentation |
Compute a smoothed empirical distribution function for objects of
class "expert"
.
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)", ...)
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. |
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.
For ogive
, a function of class "ogive"
, inheriting from the
"function"
class.
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (1998), Loss Models, From Data to Decisions, Wiley.
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).
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)