selectiongain (version 2.0.1)

multistagetp: Function for calculating the truncation point

Description

This function calculates the coordinates of the truncation point Q for given selected fractions A. The R function uniroot in core package stats is called internally to solve the truncation point equations.

Usage

multistagetp(alpha, corx, alg)

Arguments

alpha

Probability vector $\vec{\alpha}$ for random variable X. In plant breeding, it is also called the selected fraction.

corx

Correlation matrix of X.

alg

It decides which algorithm will be used, the Genz and Bretz' algorithm is used by default. The Miwa's algorithm can be optional (Mi. et al. 2009; Genz. et al. 2010).

Value

• The out come is a vector for the coordinates.

Details

This function calculates the non-equi coordinate quantile vector $Q={q_{1},q_{2},...,q_{n}}$ for a multivariate normal distribution from a given alpha vector $\vec{\alpha}={ \alpha_{1},\alpha_{2},...,\alpha_{n} }$. It can be compared with the function qmvnorm() in R-package mvtnorm, which calculates the equi coordinate quantile $q$ for multi-variate normal distribution from a given alpha scalar. More details are in the JSS paper section 3.2.

References

A. Genz and F. Bretz. Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195, Springer-Verlag, Heidelberg, 2009. A. Genz, F. Bretz, T. Miwa, X. Mi, F. Leisch, F. Scheipl and T. Hothorn. mvtnorm: Multivariate normal and t distributions. R package version 0.9-9, 2010. G.M. Tallis. Moment generating function of truncated multi-normal distribution. Journal of the Royal Statistical Society, Series B, 23(1):223-229, 1961. H.F. Utz. Mehrstufenselecktion in der Pflanzenzuechtung. Doctor thesis, University Hohenheim, 1969. W.G. Cochran. Improvent by means of selection. In: Proceedings Second Berkeley Symposium on Math Stat Prof, pp449-470, 1951 X. Mi, T. Miwa and T. Hothorn. Implement of Miwa's analytical algorithm of multi-normal distribution, R Journal, 1:37-39, 2009. X. Mi, H.F. Utz. and A.E. Melchinger. R package selectiongain: A tool for efficient calculation and optimization of the expected gain from multi-stage selection. J Stat Softw. (submitted)

See Also

selectiongain(), qnorm()

Examples

dim=3
 alpha=rep(0,dim)

 alpha[1] = 0.3333
 alpha[2] = 0.25
 alpha[3] = 0.2

corr=diag(3)

corr12=0.3016
corr[1,2]=corr12
corr[2,1]=corr12

corr13=0.5630
corr[1,3]=corr13
corr[3,1]=corr13

corr23=0.5630
corr[2,3]=corr23
corr[3,2]=corr23

multistagetp(alpha,corx=corr)