boot_sdm {CAISEr} R Documentation

## Bootstrap the sampling distribution of the mean

### Description

Bootstraps the sampling distribution of the means for a given vector of observations

### Usage

```boot_sdm(x, boot.R = 999, ncpus = 1, seed = NULL)
```

### Arguments

 `x` vector of observations `boot.R` number of bootstrap resamples `ncpus` number of cores to use `seed` seed for the PRNG

### Value

vector of bootstrap estimates of the sample mean

### References

• A.C. Davison, D.V. Hinkley: Bootstrap methods and their application. Cambridge University Press (1997)

• F. Campelo, F. Takahashi: Sample size estimation for power and accuracy in the experimental comparison of algorithms. Journal of Heuristics 25(2):305-338, 2019.

### Author(s)

Felipe Campelo (fcampelo@ufmg.br, f.campelo@aston.ac.uk)

### Examples

```x <- rnorm(15, mean = 4, sd = 1)
my.sdm <- boot_sdm(x)
hist(my.sdm, breaks = 30)
qqnorm(my.sdm, pch = 20)

x <- runif(12)
my.sdm <- boot_sdm(x)
qqnorm(my.sdm, pch = 20)

# Convergence of the SDM to a Normal distribution as sample size is increased
X <- rchisq(1000, df = 3)
x1 <- rchisq(10, df = 3)
x2 <- rchisq(20, df = 3)
x3 <- rchisq(40, df = 3)
par(mfrow = c(2, 2))
plot(density(X), main = "Estimated pop distribution");
hist(boot_sdm(x1), breaks = 25, main = "SDM, n = 10")
hist(boot_sdm(x2), breaks = 25, main = "SDM, n = 20")
hist(boot_sdm(x3), breaks = 25, main = "SDM, n = 40")
par(mfrow = c(1, 1))
```

[Package CAISEr version 1.0.16 Index]