fixedpointproperty (version 1.0)

normMix: Gaussian binary mixture distribution

Description

Density, distribution, function, quantile function, and random generation for the mixture of two Gaussian distributions with mixture proportion p and 1-p.

Usage

dnormMix(x, mean=c(0,1), sd=c(1,1), p=1)
pnormMix(x, mean=c(0,1), sd=c(1,1), p=1)
qnormMix(x, mean=c(0,1), sd=c(1,1), p=1)
rnormMix(n, mean=c(0,1), sd=c(1,1), p=1)

Value

dnormMix gives the density, pnormMix gives the distribution function, qnormMix gives the quantile function, and rnormMix generates random deviates.

Arguments

x

vector of quantiles or probabilities.

n

number of observations.

mean

vector of two means.

sd

vector of standard deviations.

p

mixture proportion of the first distribution (the second has proportion 1-p).

Author

Leendert van Maanen ([e-mail])

References

Van Maanen, L., De Jong, R., Van Rijn, H (2014). How to assess the existence of competing strategies in cognitive tasks: A primer on the fixed-point property. PLOS One, 9, e106113

Van Maanen, L. Couto, J. & Lebetron, M. (2016). Three boundary conditions for computing the fixed-point property in binary mixture data. PLOS One, 11, e0167377.

Examples

## the default value for p reduces this function to a normal distribution
dnormMix(1) == dnorm(1)

## plot that illustrates the fixed-point property
p <- c(.8,.5,.2)
m <- c(0,1); s <- c(1,2)
plot(function(X) {dnormMix(X, m, s, p[1])}, -5,10, ylab="Density",xlab="x", bty='L')
for (i in 2:3) {
  plot(function(X) {dnormMix(X, m, s, p[i])},-5,10, add=TRUE, lty=i, lwd=2)
}
legend("topright", legend=paste("p=",p,sep=''), lty=1:3, lwd=2, bty='n')