PoweR (version 1.0.7)

law0014.AverageUnif: The Average Uniform Distribution

Description

Random generation for the Average Uniform distribution with parameters size, a and b.

This generator is called by function gensample to create random variables based on its parameter.

Details

If size, a and b are not specified they assume the default values of 2, 0 and 1.

The Average Uniform distribution has density: $$ \frac{k^k}{(k-1)!}\sum_{j=0}^{\lfloor k\frac{x-a}{b-a} \rfloor}(-1)^j{k \choose j}(\frac{x-a}{b-a}-\frac{j}{k})^{k-1} $$ where size = k and for \(a \le x \le b\).

References

Pierre Lafaye de Micheaux, Viet Anh Tran (2016). PoweR: A Reproducible Research Tool to Ease Monte Carlo Power Simulation Studies for Studies for Goodness-of-fit Tests in R. Journal of Statistical Software, 69(3), 1--42. doi:10.18637/jss.v069.i03

Quesenberry and Miller (1977), Power studies of some tests for uniformity, Journal of Statistical Computation and Simulation, 5(3), 169--191 (see p. 179)

See Also

law0007.Uniform for the Uniform distribution.

Distributions for other standard distributions.

Examples

# NOT RUN {
res <- gensample(14,10000,law.pars=c(9,2,3))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }