Estimation of the probability left outside the simplex when using the alpha-transformation {Compositional}

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.

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.

Value

The estimated probability left outside the simplex.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

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

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)