qqunif {gap}

Q-Q plot for uniformly distributed random variable

Description

Q-Q plot for uniformly distributed random variable

Usage

qqunif(
  u,
  type = "unif",
  logscale = TRUE,
  base = 10,
  col = palette()[4],
  lcol = palette()[2],
  ci = FALSE,
  alpha = 0.05,
  ...
)

Arguments

u

a vector of uniformly distributed random variables.

type

string option to specify distribution: "unif"=uniform, "exp"=exponential.

logscale

to use logscale.

base

the base of the log function.

col

color for points.

lcol

color for the diagonal line.

ci

logical option to show confidence interval.

alpha

1-confidence level, e.g., 0.05.

...

other options as appropriae for the qqplot function.

Details

This function produces Q-Q plot for a random variable following uniform distribution with or without using log-scale. Note that the log-scale is by default for type "exp", which is a plot based on exponential order statistics. This appears to be more appropriate than the commonly used procedure whereby the expected value of uniform order statistics is directly log-transformed.

Value

The returned value is a list with components of a qqplot:

• x expected value for uniform order statistics or its -log(,base) counterpart.

• y observed value or its -log(,base) counterpart.

Author(s)

Jing Hua Zhao

References

Balakrishnan N, Nevzorov VB (2003). A Primer on Statistical Distributions. Wiley, Hoboken, N.J. ISBN 9780471427988, https://www.amazon.com/dp/B011SJAWXG/.

Casella G, Berger RL (2002). Statistical Inference, 2 edition. Duxbury. ISBN 978-0-534-24312-8, https://www.amazon.com/dp/7111109457/.

Davison AC (2003). Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge University Press (2003-08-04). https://www.amazon.com/dp/B01A0BLZKM/.

See Also

qqfun

Examples

## Not run: 
# Q-Q Plot for 1000 U(0,1) r.v., marking those <= 1e-5
u_obs <- runif(1000)
r <- qqunif(u_obs,pch=21,bg="blue",bty="n")
u_exp <- r$y
hits <- u_exp >= 2.30103
points(r$x[hits],u_exp[hits],pch=21,bg="green")
legend("topleft",sprintf("GC.lambda=\

## End(Not run)