R: Empirical Limited Expected Value

elev {actuar} | R Documentation

## Empirical Limited Expected Value

### Description

Compute the empirical limited expected value for individual or grouped data.

### Usage

    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")

### Arguments

`x` | a vector or an object of class `"grouped.data"` (in which case only the first column of frequencies is used); for the methods, an object of class `"elev"`, typically.
`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.

### Details

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.

### Value

For `elev`, a function of class `"elev"`, 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; `stepfun` for related documentation (even though the empirical LEV is not a step function).

### Examples

    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)

[Package actuar version 3.1-2 Index]