farebrother {CompQuadForm} | R Documentation |
Ruben/Farebrother method
Description
Distribution function (survival function in fact) of quadratic forms in normal variables using Farebrother's algorithm.
Usage
farebrother(q, lambda, h = rep(1, length(lambda)),
delta = rep(0, length(lambda)), maxit = 100000,
eps = 10^(-10), mode = 1)
Arguments
q |
value point at which distribution function is to be evaluated |
lambda |
the weights |
h |
vector of the respective orders of multiplicity |
delta |
the non-centrality parameters |
maxit |
the maximum number of term K in equation below |
eps |
the desired level of accuracy |
mode |
if 'mode' > 0 then |
Details
Computes P[Q>q] where Q=\sum_{j=1}^n\lambda_j\chi^2(m_j,\delta_j^2)
. P[Q<q] is approximated by \sum_k=0^{K-1} a_k P[\chi^2(m+2k)<q/\beta]
where m=\sum_{j=1}^n m_j
and \beta
is an arbitrary constant (as given by argument mode).
Value
dnsty |
the density of the linear form |
ifault |
the fault indicator. -i: one or more of the constraints
|
, m_i>0
and \delta_i^2\geq0
is not
satisfied. 1: non-fatal underflow of a_0
. 2: one or more of the
constraints n>0
, q>0
, maxit>0
and eps>0
is not
satisfied. 3: the current estimate of the probability is greater than
2. 4: the required accuracy could not be obtained in 'maxit'
iterations. 5: the value returned by the procedure does not satisfy
0\leq RUBEN\leq 1
. 6: 'dnsty' is negative. 9: faults 4 and
5. 10: faults 4 and 6. 0: otherwise.
Qq |
|
Author(s)
Pierre Lafaye de Micheaux (lafaye@dms.umontreal.ca) and Pierre Duchesne (duchesne@dms.umontreal.ca)
References
P. Duchesne, P. Lafaye de Micheaux, Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods, Computational Statistics and Data Analysis, Volume 54, (2010), 858-862
Farebrother R.W., Algorithm AS 204: The distribution of a Positive Linear Combination of chi-squared random variables, Journal of the Royal Statistical Society, Series C (applied Statistics), Vol. 33, No. 3 (1984), p. 332-339
Examples
# Some results from Table 3, p.327, Davies (1980)
1 - farebrother(1, c(6, 3, 1), c(1, 1, 1), c(0, 0, 0))$Qq