# elev: Empirical Limited Expected Value In actuar: Actuarial Functions and Heavy Tailed Distributions

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```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, …, 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

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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) ```

### Example output ```Attaching package: 'actuar'

The following object is masked from 'package:grDevices':

cm

Empirical LEV
Call: elev(x = gdental)
cj[1:11] =      0,     25,     50,  ...,   2500,   4000
Empirical LEV:	  10 unique values with summary
Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
0.0    75.0   250.0   915.9  1250.0  4000.0
    0   25   50  100  150  250  500 1000 1500 2500 4000
   0.00000  24.00794  45.99868  84.16005 115.77381 164.84788 238.26058
 299.76852 324.90079 347.38757 353.33995
  69.80026 142.46032 339.78175
```

actuar documentation built on May 31, 2021, 9:10 a.m.