law0014.AverageUnif {PoweR} | R Documentation |
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
.
Author(s)
P. Lafaye de Micheaux, V. A. Tran
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
res <- gensample(14,10000,law.pars=c(9,2,3))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)