RNGMIX-methods: Random Univariate or Multivariate Finite Mixture Generation

Description

Returns as default the RNGMIX univariate or multivariate random datasets for mixtures of conditionally independent normal, lognormal, Weibull, gamma, Gumbel, binomial, Poisson, Dirac, uniform or von Mises component densities. If model equals "RNGMVNORM" multivariate random datasets for mixtures of multivariate normal component densities with unrestricted variance-covariance matrices are returned.

Usage

# S4 method for RNGMIX
RNGMIX(model = "RNGMIX", Dataset.name = character(),
       rseed = -1, n = numeric(), Theta = list(), ...)
## ... and for other signatures

Value

Returns an object of class RNGMIX or RNGMVNORM.

Arguments

model: see Methods section below.
Dataset.name: a character vector containing list names of data frames of size $n \times d$ that d-dimensional datasets are written in.
rseed: set the random seed to any negative integer value to initialize the sequence. The first file in Dataset.name corresponds to it. For each next file the random seed is decremented $r_{seed} = r_{seed} - 1$ . The default value is -1.
n: a vector containing numbers of observations in classes $n_{l}$ , where number of observations $n = \sum_{l = 1}^{c} n_{l}$ .
Theta: a list containing $c$ parametric family types pdfl. One of "normal", "lognormal", "Weibull", "gamma", "Gumbel", "binomial", "Poisson", "Dirac", "uniform" or circular "vonMises" defined for $0 \leq y_{i} \leq 2 π$ . Component parameters theta1.l follow the parametric family types. One of $μ_{i l}$ for normal, lognormal, Gumbel and von Mises distributions, $θ_{i l}$ for Weibull, gamma, binomial, Poisson and Dirac distributions and $a$ for uniform distribution. Component parameters theta2.l follow theta1.l. One of $σ_{i l}$ for normal, lognormal and Gumbel distributions, $β_{i l}$ for Weibull and gamma distributions, $p_{i l}$ for binomial distribution, $κ_{i l}$ for von Mises distribution and $b$ for uniform distribution. Component parameters theta3.l follow theta2.l. One of $ξ_{i l} \in {- 1, 1}$ for Gumbel distribution.
...: currently not used.

Methods

signature(model = "RNGMIX"): a character giving the default class name "RNGMIX" for mixtures of conditionally independent normal, lognormal, Weibull, gamma, Gumbel, binomial, Poisson, Dirac, uniform or von Mises component densities.
signature(model = "RNGMVNORM"): a character giving the class name "RNGMVNORM" for mixtures of multivariate normal component densities with unrestricted variance-covariance matrices.

Author

Marko Nagode

Details

RNGMIX is based on the "Minimal" random number generator ran1 of Park and Miller with the Bays-Durham shuffle and added safeguards that returns a uniform random deviate between 0.0 and 1.0 (exclusive of the endpoint values).

References

W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery. Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge, 1992.

Examples

Run this code

devAskNewPage(ask = TRUE)

# Generate and print multivariate normal datasets with diagonal
# variance-covariance matrices.

n <- c(75, 100, 125, 150, 175)

Theta <- new("RNGMIX.Theta", c = 5, pdf = rep("normal", 4))

a.theta1(Theta, 1) <- c(10, 12, 10, 12)
a.theta1(Theta, 2) <- c(8.5, 10.5, 8.5, 10.5)
a.theta1(Theta, 3) <- c(12, 14, 12, 14)
a.theta1(Theta, 4) <- c(13, 15, 7, 9)
a.theta1(Theta, 5) <- c(7, 9, 13, 15)
a.theta2(Theta, 1) <- c(1, 1, 1, 1)
a.theta2(Theta, 2) <- c(1, 1, 1, 1)
a.theta2(Theta, 3) <- c(1, 1, 1, 1)
a.theta2(Theta, 4) <- c(2, 2, 2, 2)
a.theta2(Theta, 5) <- c(3, 3, 3, 3)

simulated <- RNGMIX(Dataset.name = paste("simulated_", 1:25, sep = ""),
  rseed = -1,
  n = n,
  Theta = a.Theta(Theta))

simulated

plot(simulated, pos = 22, nrow = 2, ncol = 3)

# Generate and print multivariate normal datasets with unrestricted
# variance-covariance matrices.

n <- c(200, 50, 50)

Theta <- new("RNGMVNORM.Theta", c = 3, d = 3)

a.theta1(Theta, 1) <- c(0, 0, 0)
a.theta1(Theta, 2) <- c(-6, 3, 6)
a.theta1(Theta, 3) <- c(6, 6, 4)
a.theta2(Theta, 1) <- c(9, 0, 0, 0, 4, 0, 0, 0, 1)
a.theta2(Theta, 2) <- c(4, -3.2, -0.2, -3.2, 4, 0, -0.2, 0, 1)
a.theta2(Theta, 3) <- c(4, 3.2, 2.8, 3.2, 4, 2.4, 2.8, 2.4, 2)

simulated <- RNGMIX(model = "RNGMVNORM",
  Dataset.name = paste("simulated_", 1:2, sep = ""),
  rseed = -1,
  n = n,
  Theta = a.Theta(Theta))

simulated

plot(simulated, pos = 2, nrow = 3, ncol = 1)

# Generate and print multivariate mixed continuous-discrete datasets.

n <- c(400, 100, 500)

Theta <- new("RNGMIX.Theta", c = 3, pdf = c("lognormal", "Poisson", "binomial", "Weibull"))

a.theta1(Theta, 1) <- c(1, 2, 10, 2)
a.theta1(Theta, 2) <- c(3.5, 10, 10, 10)
a.theta1(Theta, 3) <- c(2.5, 15, 10, 25)
a.theta2(Theta, 1) <- c(0.3, NA, 0.9, 3)
a.theta2(Theta, 2) <- c(0.2, NA, 0.1, 7)
a.theta2(Theta, 3) <- c(0.4, NA, 0.7, 20)

simulated <- RNGMIX(Dataset.name = paste("simulated_", 1:5, sep = ""),
  rseed = -1,
  n = n,
  Theta = a.Theta(Theta))

simulated

plot(simulated, pos = 4, nrow = 2, ncol = 3)

# Generate and print univariate mixed Weibull dataset.

n <- c(75, 100, 125, 150, 175)

Theta <- new("RNGMIX.Theta", c = 5, pdf = "Weibull")

a.theta1(Theta) <- c(12, 10, 14, 15, 9)
a.theta2(Theta) <- c(2, 4.1, 3.2, 7.1, 5.3)

simulated <- RNGMIX(Dataset.name = "simulated",
  rseed = -1,
  n = n,
  Theta = a.Theta(Theta))

simulated

plot(simulated, pos = 1)

# Generate and print multivariate normal datasets with unrestricted
# variance-covariance matrices.

# Set dimension, dataset size, number of components and seed.

d <- 2; n <- 1000; c <- 10; set.seed(123)

# Component weights are generated.

w <- runif(c, 0.1, 0.9); w <- w / sum(w)

# Set range of means and rang of eigenvalues.

mu <- c(-100, 100); lambda <- c(1, 100)

# Component means and variance-covariance matrices are calculated.

Mu <- list(); Sigma <- list()

for (l in 1:c) {
  Mu[[l]] <- runif(d, mu[1], mu[2])
  Lambda <- diag(runif(d, lambda[1], lambda[2]), nrow = d, ncol = d)
  P <- svd(matrix(runif(d * d, -1, 1), nc = d))$u
  Sigma[[l]] <- P 
}

# Numbers of observations are calculated and component means and 
# variance-covariance matrices are stored.

n <- round(w * n); Theta <- list()

for (l in 1:c) {
  Theta[[paste0("pdf", l)]] <- rep("normal", d)
  Theta[[paste0("theta1.", l)]] <- Mu[[l]]
  Theta[[paste0("theta2.", l)]] <- as.vector(Sigma[[l]])
}

# Dataset is generated.

simulated <- RNGMIX(model = "RNGMVNORM", Dataset.name = "mvnorm_1",
  rseed = -1, n = n, Theta = Theta)

plot(simulated)

# Generate and print bivariate mixed uniform-Gumbel dataset.

n <- c(100, 150)

Theta <- new("RNGMIX.Theta", c = 2, pdf = c("uniform", "Gumbel"))

a.theta1(Theta, l = 1) <- c(2, 10)
a.theta2(Theta, l = 1) <- c(10, 2.3)
a.theta3(Theta, l = 1) <- c(NA, 1.0)
a.theta1(Theta, l = 2) <- c(10, 50)
a.theta2(Theta, l = 2) <- c(30, 4.2)
a.theta3(Theta, l = 2) <- c(NA, -1.0)

simulated <- RNGMIX(Dataset.name = paste("simulated_", 1, sep = ""),
  rseed = -1,
  n = n,
  Theta = a.Theta(Theta))
  
plot(simulated)

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