Distribution functions for the three-parameter mixture model (mixture3p)

Density, distribution, and random generation functions for the three-parameter mixture model with the location of mu, precision of memory representations kappa, probability of recalling items from memory p_mem, and probability of recalling non-targets p_nt.

Usage

dmixture3p(
  x,
  mu = c(0, 2, -1.5),
  kappa = 5,
  p_mem = 0.6,
  p_nt = 0.2,
  log = FALSE
)

pmixture3p(q, mu = c(0, 2, -1.5), kappa = 5, p_mem = 0.6, p_nt = 0.2)

qmixture3p(p, mu = c(0, 2, -1.5), kappa = 5, p_mem = 0.6, p_nt = 0.2)

rmixture3p(n, mu = c(0, 2, -1.5), kappa = 5, p_mem = 0.6, p_nt = 0.2)

Arguments

x

Vector of observed responses

mu

Vector of locations. First value represents the location of the target item and any additional values indicate the location of non-target items.

kappa

Vector of precision values

p_mem

Vector of probabilities for memory recall

p_nt

Vector of probabilities for swap errors

log

Logical; if TRUE, values are returned on the log scale.

q

Vector of quantiles

p

Vector of probability

n

Number of observations to generate data for

Value

dmixture3p gives the density of the three-parameter mixture model, pmixture3p gives the cumulative distribution function of the two-parameter mixture model, qmixture3p gives the quantile function of the two-parameter mixture model, and rmixture3p gives the random generation function for the two-parameter mixture model.

References

Bays, P. M., Catalao, R. F. G., & Husain, M. (2009). The precision of visual working memory is set by allocation of a shared resource. Journal of Vision, 9(10), 7.

Examples

# generate random samples from the mixture3p model and overlay the density
r <- rmixture3p(10000, mu = c(0, 2, -1.5), kappa = 4, p_mem = 0.6, p_nt = 0.2)
x <- seq(-pi,pi,length.out=10000)
d <- dmixture3p(x, mu = c(0, 2, -1.5), kappa = 4, p_mem = 0.6, p_nt = 0.2)
hist(r, breaks=60, freq=FALSE)
lines(x,d,type="l", col="red")