Empirical Limited Expected Value
Compute the empirical limited expected value for individual or grouped data.
elev(x, ...)
## Default S3 method:
elev(x, ...)
## S3 method for class 'grouped.data'
elev(x, ...)
## S3 method for class 'elev'
print(x, digits = getOption("digits") - 2, ...)
## S3 method for class 'elev'
summary(object, ...)
## S3 method for class 'elev'
knots(Fn, ...)
## S3 method for class 'elev'
plot(x, ..., main = NULL, xlab = "x", ylab = "Empirical LEV")x |
a vector or an object of class |
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 limited expected value (LEV) at u of a random variable X is E[X ^ u] = E[min(X, u)]. For individual data x[1], …, x[n], the empirical LEV En[X ^ u] is thus
En[X ^ u] = (sum(x[j] < u; 1) + sum(x[j] >= u; u))/n.
Methods of elev exist for individual data or for grouped data
created with grouped.data. The formula in this case is
too long to show here. See the reference for details.
For elev, a function of class "elev", 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;
stepfun for related documentation (even though the
empirical LEV is not a step function).
data(gdental) lev <- elev(gdental) lev summary(lev) knots(lev) # the group boundaries lev(knots(lev)) # empirical lev at boundaries lev(c(80, 200, 2000)) # and at other limits plot(lev, type = "o", pch = 16)
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