Ogive for Grouped Data
Compute a smoothed empirical distribution function for grouped data.
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)", ...)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. |
The ogive is a linear interpolation of the empirical cumulative distribution function.
The equation of the ogive is
Gn(x) = 1/(c[j] - c[j-1]) * [(c[j] - x) Fn(c[j-1]) + (x - c[j-1]) Fn(c[j])]
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).
## 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)
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