Compositional (version 5.5)

Estimation of the probability left outside the simplex when using the alpha-transformation: Estimation of the probability left outside the simplex when using the alpha-transformation

Description

Estimation of the probability left outside the simplex when using the alpha-transformationn.

Usage

probout(mu, su, a)

Arguments

mu

The mean vector.

su

The covariance matrix.

a

The value of \(\alpha\).

Value

The estimated probability left outside the simplex.

Details

When applying the \(\alpha\)-transformation based on a multivariate normal there might be probability left outside the simplex as the space of this transformation is a subspace of the Euclidean space. The function estimates the missing probability via Monte Carlo simulation using 40 million generated vectors.

References

Tsagris M. and Stewart C. (2020). A folded model for compositional data analysis. Australian and New Zealand Journal of Statistics, 62(2): 249-277. https://arxiv.org/pdf/1802.07330.pdf

Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4th Compositional Data Analysis Workshop, Girona, Spain. https://arxiv.org/pdf/1106.1451.pdf

See Also

alfa, alpha.mle, a.est, rfolded

Examples

# NOT RUN {
s <-  c(0.1490676523, -0.4580818209,  0.0020395316, -0.0047446076, -0.4580818209,
1.5227259250,  0.0002596411,  0.0074836251,  0.0020395316,  0.0002596411,
0.0365384838, -0.0471448849, -0.0047446076,  0.0074836251, -0.0471448849,
0.0611442781)
s <- matrix(s, ncol = 4)
m <- c(1.715, 0.914, 0.115, 0.167)
probout(m, s, 0.5)
# }