# 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 = 1}^n x_j^k.

For grouped data with group boundaries c_0, c_1, \dots, c_r and group frequencies n_1, \dots, n_r, the kth empirical moment is

\frac{1}{n} \sum_{j = 1}^r \frac{n_j (c_j^{k + 1} - c_{j - 1}^{k + 1})}{% (k + 1) (c_j - c_{j - 1})},

where n = \sum_{j = 1}^r 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 Nov. 8, 2023, 9:06 a.m.