actuar (version 3.3-4)

emm: Empirical Moments

Description

Raw empirical moments for individual and grouped data.

Usage

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

Value

A named vector or matrix of moments.

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.

Author

Vincent Goulet and Mathieu Pigeon

Details

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

For individual data, the \(k\)th 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 \(k\)th 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 \(n = \sum_{j = 1}^r n_j\).

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)