proddnf: The product of multiple doubly non-central F's distribution.

Description

Density, distribution function, quantile function and random generation for the product of multiple independent doubly non-central F variates.

Usage

dproddnf(x, df1, df2, ncp1, ncp2, log = FALSE, order.max=4)
pproddnf(q, df1, df2, ncp1, ncp2, lower.tail = TRUE, log.p = FALSE, order.max=4)
qproddnf(p, df1, df2, ncp1, ncp2, lower.tail = TRUE, log.p = FALSE, order.max=4)
rproddnf(n, df1, df2, ncp1, ncp2)

Value

dproddnf gives the density, pproddnf gives the distribution function, qproddnf gives the quantile function, and rproddnf generates random deviates.

Invalid arguments will result in return value NaN with a warning.

Arguments

x, q: vector of quantiles.
df1, df2: the vectors of the degrees of freedom for the numerator and denominator. We do not recycle these versus the x,q,p,n.
ncp1, ncp2: the vectors of the non-centrality parameters for the numerator and denominator. We do not recycle these versus the x,q,p,n.
log: logical; if TRUE, densities $f$ are given as $\mbox{log}(f)$.
order.max: the order to use in the approximate density, distribution, and quantile computations, via the Gram-Charlier, Edeworth, or Cornish-Fisher expansion.
p: vector of probabilities.
n: number of observations.
log.p: logical; if TRUE, probabilities p are given as $\mbox{log}(p)$.
lower.tail: logical; if TRUE (default), probabilities are $P[X \le x]$, otherwise, $P[X > x]$.

Author

Steven E. Pav shabbychef@gmail.com

Details

Let $$x_j \sim F\left(\delta_{1,j},\delta_{2,j},\nu_{1,j},\nu_{2,j}\right)$$ be independent doubly non-central F variates with non-centrality parameters $\delta_{i,j}$ and degrees of freedom $\nu_{i,j}$ for $i=1,2,\ldots,I$ and $j=1,2$. Then $$Y = \prod_j x_j$$ takes a product of doubly non-central F's distribution. We take the parameters of this distribution as the four $I$ length vectors of the two degrees of freedom and the two non-centrality parameters.

References

Pav, Steven. Moments of the log non-central chi-square distribution. https://arxiv.org/abs/1503.06266

Examples

Run this code

df1 <- c(10,20,5)
df2 <- c(1000,500,150)
ncp1 <- c(1,0,2.5)
ncp2 <- c(0,1.5,5)

rv <- rproddnf(500, df1=df1,df2=df2,ncp1=ncp1,ncp2=ncp2)
d1 <- dproddnf(rv, df1=df1,df2=df2,ncp1=ncp1,ncp2=ncp2)
# \donttest{
plot(rv,d1)
# }
p1 <- pproddnf(rv, df1=df1,df2=df2,ncp1=ncp1,ncp2=ncp2)
# should be nearly uniform:
# \donttest{
plot(ecdf(p1))
# }
q1 <- qproddnf(ppoints(length(rv)), df1=df1,df2=df2,ncp1=ncp1,ncp2=ncp2)
# \donttest{
qqplot(x=rv,y=q1)
# }

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