Get simultaneous confidence bands for a uniform QQ-plot

This will provide 100(1-a)% simultaneous confidence bands for a sample of size n. It does this by the "tail-sensitive" approach of Aldor-Noiman et al (2013), which uses simulated uniform vectors. The number of simulations is controlled by nsamp.

ts_bands(n, nsamp = 1000, a = 0.05)

Arguments

n

Sample size.

nsamp

Number of simulation repetitions.

a

The significance level.

Value

A list of length 3. The $lower and $upper confidence limits at uniform quantiles $q.

Details

The procedure used is described in Aldor-Noiman et al (2013). But note that they have a mistake in their paper. Step (e) of their algorithm on page 254 should be the CDF of the Beta distribution, not the quantile function.

References

• Aldor-Noiman, S., Brown, L. D., Buja, A., Rolke, W., & Stine, R. A. (2013). The power to see: A new graphical test of normality. The American Statistician, 67(4), 249-260.

Author

David Gerard

Examples

ts <- ts_bands(100)

graphics::plot(x = ts$q,
               y = ts$upper,
               type = "l",
               xlim = c(0, 1),
               ylim = c(0, 1),
               xlab = "Theoretical Quantiles",
               ylab = "Empirical Quantiles")
graphics::lines(x = ts$q, y = ts$lower)
graphics::lines(x = ts$q, y = ts$q, lty = 2)