Three dimensional plots using rgl package

Good topic Tanvir. Thanks for posting.

If you add some reproducible data that would benefit average users like me. For example, in you code what is X, Y, Z? I assume that they are vectors, right?

In short, an article is most useful if it is self contained. An example with a real example helps understanding things better.

Another thing is, if you have a main figure for the article, don't show it again in the body of the article. This will save some bandwidth for people in Bangladesh. Instead, you can just refer to the figure above and give the code near the bottom.

Keep up the good work.

Here is one particular example of 3d plots using not-so-fancy packages (basic and lattice):

A brief description of the problem:

gk-distribution is a broader class of distribution with parameters G (skewness) and K (kurtosis). In this family of distribution, G = 0 and K = 0 gives a special case - which is popularly known as normal distribution (skewness and kurtosis values are zero). Thus, to check the performance of a normality test such asPearson Chi-square test, a simple strategy would be to generate data from gk-distribution with various values of G and K, and then see whether according to the test, those data follows normality or not, in the entire parameter grid. Similar strategy would be also applicable to check the effect of sample size. As we know from theory, the greater the sample size, the better the power curves should be. Therefore, in this analysis, I generate data from gk-distribution using sample sizes 5, 10, 15 and 30. Also to produce the grid, I used values from -5 to +5 for G, and -0.5 to 5 for K. Since I am basically interested what happens near (0, 0) location, the grid is tighter there. Since this requires 3D plots to show the powers of the parameter grid, I used both basic and lattice plots. Eventually it can be shown that the more the sample size, the better the powers, since the rejection rate near (G, K) = (0, 0) is very low for higher sample sizes, and very high in all other locations. However, when the sample size gets smaller, the performance of the powers are not very encouraging in favor of this test.

Click on the hyperlinked code to see the output:

# load required packages
require(nortest)
require(lattice)

# Setting the sample size and number of simulations.
# If the "sampleSize.fix" value is changed and sourced from R,
# this program will automatically generate graphs
# for specifies sample size
sampleSize.fix = 30 # The other values of sample size are 5, 10, 15
simNum.fix = 100

# Function to generate gk distribution data
gk <- function(G, K, simNum, sampleSize){
rejectionCount <- rep(0,simNum)
for(i in 1:simNum){
z <- rnorm(sampleSize, 0, 1)
gkGenerated <- 0+1*z*(1+.83*(1-exp(-G*z))/(1+exp(-G*z)))*(1+z^2)**K
gkTest <- pearson.test(gkGenerated)
pearsonPvalue <- gkTest\$p.value
if(pearsonPvalue <= 0.05) {
rejectionCount[i] <- 1
}
else {
rejectionCount[i] <- 0
}
}
power <- mean(rejectionCount)
return(power)
}

# Making the grid with G (skewness) and K (kurtosis) parameters
G <- c(-5, -4, -3, -2, -1.5, -1, -0.75, -0.5, -0.25,
0, 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5)
K <- c(-0.5, -0.25, 0, 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5)
lg <- length(G)
lk <- length(K)
parameterGrid <- expand.grid(Ggrid = G, Kgrid = K)
parameterGrid <- as.data.frame(parameterGrid)
ggrid <- parameterGrid[[1]]
kgrid <- parameterGrid[[2]]

# Linking gk function with the parameter grid
gkPower <- function(x, simNum, sampleSize){
gk(ggrid[x], kgrid[x], simNum, sampleSize)
}

gkPowerStore <- double(length = (lg*lk))
# storing the powers of analysis
for (i in 1:(lg*lk)) {
gkPowerStore[i] <- gkPower(i, simNum = simNum.fix,
sampleSize = sampleSize.fix)
cat("iteration", i, "\n")
}
# converting the vector into matrix for convenience of making the plots
powerMatrix <- matrix(gkPowerStore, nrow=lg, ncol=lk, byrow=F)

# producing basic plots
x11()
persp(G, K, powerMatrix, theta = 30, phi = 30,
expand = 0.5, d = 1, ltheta = 120,
shade = 0.5, ticktype = "detailed",
xlab = "Parameter G", ylab = "Parameter K",
zlab = "Power", col = "lightblue",
main = "Basic Graph", sub = paste("Sample size =", sampleSize.fix))
dev.copy2pdf(file = paste("basic", sampleSize.fix, ".pdf", sep = ""),
onefile = TRUE, paper = "a4",family = "Helvetica",
pointsize=1, fonts = "Helvetica")
dev.copy2eps(file = paste("basic", sampleSize.fix, ".eps", sep = ""),
onefile = TRUE, paper = "a4",family = "Helvetica",
pointsize=1, print.it = FALSE, fonts ="Helvetica")
dev.off()

# producing lattice plots
x11()
wireframe(powerMatrix~parameterGrid\$Kgrid*parameterGrid\$Ggrid,
main = "Lattice Graph", xlab = "Parameter K", ylab = "Parameter G",
zlab = "Power", shade = T,
sub = paste("Sample size =", sampleSize.fix))
dev.copy2pdf(file = paste("lattice", sampleSize.fix, ".pdf", sep = ""),
onefile = TRUE, paper = "a4",family = "Helvetica",
pointsize=1, fonts = "Helvetica")
dev.copy2eps(file = paste("lattice", sampleSize.fix, ".eps", sep = ""),
onefile = TRUE, paper = "a4",family = "Helvetica", pointsize=1,
print.it = FALSE, fonts ="Helvetica")
dev.off()

Warning: Running this piece of code will generate 4 graphs in your R working directory (see getwd).