# emm: Empirical Moments In actuar: Actuarial Functions and Heavy Tailed Distributions

 emm 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, c, …, c[r] and group frequencies n, …, n[r], the kth empirical moment is

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

`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)
```

actuar documentation built on July 16, 2022, 9:05 a.m.