ogive {actuar} | R Documentation |
Ogive for Grouped Data
Description
Compute a smoothed empirical distribution function for grouped data.
Usage
ogive(x, ...)
## Default S3 method:
ogive(x, y = NULL, breaks = "Sturges", nclass = NULL, ...)
## S3 method for class 'grouped.data'
ogive(x, ...)
## 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 |
for the generic and all but the default method, an object of
class |
y |
a vector of group frequencies. |
breaks , nclass |
arguments passed to |
digits |
number of significant digits to use, see
|
Fn , object |
an R object inheriting from |
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
for and where
are the
group
boundaries and
is the empirical distribution function of
the sample.
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;
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).
Examples
## Most common usage: create ogive from grouped data object.
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) # graphical representation
## Alternative 1: create ogive directly from individual data
## without first creating a grouped data object.
ogive(dental) # automatic class boundaries
ogive(dental, breaks = c(0, 50, 200, 500, 1500, 2000))
## Alternative 2: create ogive from set of group boundaries and
## group frequencies.
cj <- c(0, 25, 50, 100, 250, 500, 1000)
nj <- c(30, 31, 57, 42, 45, 10)
ogive(cj, nj)