spence.21 {locfit} | R Documentation |

## Spencer's 21 point graduation rule.

### Description

Spencer's 21 point rule is a weighted moving average operation
for a sequence of observations equally spaced in time. The
average at time t depends on the observations at times t-11,...,t+11.

Except for boundary effects, the function will reproduce
polynomials up to degree 3.

### Usage

spence.21(y)

### Arguments

`y` |
Data vector of observations at equally spaced points. |

### Value

A vector with the same length as the input vector, representing
the graduated (smoothed) values.

### References

Spencer, J. (1904).
On the graduation of rates of sickness and mortality.
Journal of the Institute of Actuaries 38, 334-343.

### See Also

`spence.15`

,
`spencer`

,

### Examples

data(spencer)
yy <- spence.21(spencer$mortality)
plot(spencer$age, spencer$mortality)
lines(spencer$age, yy)

[Package

*locfit* version 1.1-9

Index]