| ogive {actuar} | R Documentation |
Compute a smoothed empirical distribution function for grouped data.
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)", ...)
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. |
The ogive is a linear interpolation of the empirical cumulative distribution function.
The equation of the ogive is
Gn(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 and Fn is the empirical distribution function of the sample.
For ogive, a function of class "ogive", inheriting from the
"function" class.
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (1998), Loss Models, From Data to Decisions, Wiley.
grouped.data to create grouped data objects;
quantile.grouped.data for the inverse function;
approxfun, which is used to compute the ogive;
stepfun for related documentation (even though the ogive
is not a step function).
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)