# beales: Beale's Estimator and Sample Size In funtimes: Functions for Time Series Analysis

 beales R Documentation

## Beale's Estimator and Sample Size

### Description

Beale's ratio estimator \insertCiteBeale_1962funtimes for estimating population total and confidence intervals, with an option of calculating sample size for a required relative error (`p`) or margin of error (`d`).

### Usage

``````beales(x, y, level = 0.95, N = NULL, p = NULL, d = NULL, verbose = TRUE)
``````

### Arguments

 `x` a numeric vector with quantities of interest, such as river discharge per month. Missing values (`NA`) are allowed. `y` a numeric vector with quantities of interest for which the total shall be estimated, such as total nutrient loads per month. Missing values (`NA`) are allowed. Lengths of `x` and `y` mush be the same. `level` confidence level, from 0 to 1. Default is `0.95`, that is, 95% confidence. `N` population size for which the estimate of the total `y` is required. By default, `length(x)` is used. `p` optional argument specifying the required relative error, from 0 to 1, for computing the corresponding sample size. For example, `p = 0.15` defines a 15% relative error. `d` optional argument specifying the required margin of error for computing the corresponding sample size. If both `p` and `d` are specified, only `p` is used. `verbose` logical value defining whether the output should be printed out in words. Default is set to `TRUE` to give such output.

### Value

A list with the following components:

 `estimate` Beale's estimate of the population total for the variable `y`. `se` standard error of the estimate. `CI` a vector of length 2 with a confidence interval (lower and upper value) for the estimate. `level` confidence level for the interval. `N` population size. `n` the actual sample size. `p` the relative error used for sample size calculations. Reported only if `p` was specified in the input. `d` the margin of error used for sample size calculations. Reported only if `d` was specified and `p` was not specified in the input. `nhat` estimated sample size for the given `level` and error (`p` or `d`).

### Author(s)

Vyacheslav Lyubchich, thanks to Dave Lorenz for pointing out an error in version 7 and below of the package

### References

\insertAllCited

`vignette("beales", package = "funtimes")`

### Examples

``````#Some hypothetical data for monthly river discharge
discharge <- c(NA, 50, 90, 100, 80, 90, 100, 90, 80, 70, NA, NA)
loads <- c(33, 22, 44, 48, NA, 44, 49, NA, NA, 36, NA, NA)

#Example 1:
#Estimate total annual load (12 months),
#with 90% confidence intervals