# optiallo: Optimal allocation in stratified simple random sampling In optimStrat: Choosing the Sample Strategy

## Description

Allocates a sample of size `n` using Neyman optimal allocation in Stratified Simple Random Sampling.

## Usage

 `1` ```optiallo(n, x, stratum = NULL, ...) ```

## Arguments

 `n` a positive integer indicating the desired sample size. `x` a positive numeric vector giving the values of the auxiliary variable. `stratum` a vector indicating the stratum to which every unit belongs (see ‘Details’). `...` other arguments passed to `stratify` (see ‘Details’).

## Details

Allocates a sample of size `n` using Neyman optimal allocation in Stratified Simple Random Sampling.

If `stratum==NULL`, the stratification is generated via `stratify`. Then at least the number of strata should be passed to `stratify` using the argument `H`.

## Value

A list with two elements:

 `stratum` a vector indicating the stratum to which each element belongs. `nh` a vector indicating the sample size of the strata to which each element belongs.

`stratify` for defining the stratification using the cum-sqrt-rule.

## Examples

 ```1 2 3 4 5``` ```x<- 1 + sort( rgamma(100, shape=4/9, scale=108) ) st1<- stratify(x,H=6) optiallo(n=30,x,stratum=st1) optiallo(n=30,x,H=6) ```

### Example output

```Loading required package: shiny
\$stratum
[1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2
[38] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4
[75] 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6

\$nh
[1] 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313
[9] 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313
[17] 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313
[25] 2.020313 2.020313 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141
[33] 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141
[41] 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141
[49] 4.896141 4.896141 4.896141 4.896141 4.896141 4.154946 4.154946 4.154946
[57] 4.154946 4.154946 4.154946 4.154946 4.154946 4.154946 4.154946 4.154946
[65] 4.154946 4.154946 4.154946 4.154946 4.871185 4.871185 4.871185 4.871185
[73] 4.871185 4.871185 4.871185 4.871185 4.871185 4.871185 4.871185 4.871185
[81] 4.871185 4.871185 4.871185 7.057415 7.057415 7.057415 7.057415 7.057415
[89] 7.057415 7.057415 7.057415 7.057415 7.057415 7.000000 7.000000 7.000000
[97] 7.000000 7.000000 7.000000 7.000000

\$stratum
[1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2
[38] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4
[75] 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6

\$nh
[1] 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313
[9] 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313
[17] 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313 2.020313
[25] 2.020313 2.020313 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141
[33] 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141
[41] 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141 4.896141
[49] 4.896141 4.896141 4.896141 4.896141 4.896141 4.154946 4.154946 4.154946
[57] 4.154946 4.154946 4.154946 4.154946 4.154946 4.154946 4.154946 4.154946
[65] 4.154946 4.154946 4.154946 4.154946 4.871185 4.871185 4.871185 4.871185
[73] 4.871185 4.871185 4.871185 4.871185 4.871185 4.871185 4.871185 4.871185
[81] 4.871185 4.871185 4.871185 7.057415 7.057415 7.057415 7.057415 7.057415
[89] 7.057415 7.057415 7.057415 7.057415 7.057415 7.000000 7.000000 7.000000
[97] 7.000000 7.000000 7.000000 7.000000
```

optimStrat documentation built on Nov. 11, 2020, 5:07 p.m.