R: Empirical Moments

emm {actuar} | R Documentation

## Empirical Moments

### Description

Raw empirical moments for individual and grouped data.

### Usage

    emm(x, order = 1, ...)

    ## Default S3 method:
    emm(x, order = 1, ...)

    ## S3 method for class 'grouped.data'
    emm(x, order = 1, ...)

### Arguments

`x` | a vector or matrix of individual data, or an object of class `"grouped data"`.
`order` | order of the moment. Must be positive.
`...` | further arguments passed to or from other methods.

### Details

Arguments `...` are passed to `colMeans`; `na.rm = TRUE` may be useful for individual data with missing values.

For individual data, the kth empirical moment is sum(j; x[j]^k).

For grouped data with group boundaries c[1], …, c[r] and group frequencies n[1], …, n[r], the kth empirical moment is

sum(j; (n[j]*(c[j]^k - c[j-1]^k)/(n*(k+1)*(c[j] - c[j-1])))),

where n = sum(j; n[j]).

### Value

A named vector or matrix of moments.

### 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

`mean` and `mean.grouped.data` for simpler access to the first moment.

### Examples

    ## Individual data
    data(dental)
    emm(dental, order = 1:3)

    ## Grouped data
    data(gdental)
    emm(gdental)
    x <- grouped.data(cj = gdental[, 1],
                      nj1 = sample(1:100, nrow(gdental)),
                      nj2 = sample(1:100, nrow(gdental)))
    emm(x) # same as mean(x)

[Package actuar version 3.0-0 Index]