pvrank (version 1.0)

VGGFR: Vianelli density

Description

Plots Vianelly (generalized Gaussian) density with finite range in [-1,1].

Usage

VGGFR(L1, L2, add = FALSE, lwd = 2, lty = 5, col = "blue", np = 201)

Arguments

L1

positive shape parameter.

L2

positive shape parameter. Impacts more on the tails.

add

when add=TRUE the plot is superimposed to an existing graph.

lwd

weight of the line.

lty

the type of the line.

col

color of the curve.

np

number of points to be plotted.

Value

• The value returned is a list contaning:
• st.dev
  standard deviation
• kurt
  kurtosis
• oam
  ordinate at the mode

Details

The VGGFR density is given by $$f(r;\lambda_1,\lambda_2)=\lambda_1(1-|r|^{\lambda_2})^{\lambda_1}/[2B(1/\lambda_1,\lambda_2+1)]$$ where $\lambda_1,\lambda_2>0$ and $B()$ is the beta function.

References

Tarsitano, A. and Amerise, I. L. (2013). Approximation of the null distribution of rank correlations. Submitted. Vianelli, S. (1983). The family of normal and lognormal distributions of order r. Metron, 41, 3-10.

Examples

# Density curve of a VGGFR model
VGGFR(2,12)
#
a<-ranktes(0.5, 28, "r4", "vg",FALSE, "two", FALSE)
b<-VGGFR(a$Lambda, add = FALSE, lwd = 2, lty = 5, col = "blue", np = 201)
#
# A family of density curves
VGGFR(1,2,col="black")
La<-seq(1,6,0.5);Lg<-seq(0,1,1/12)
for (L1 in La){
	c2<-gray(Lg, alpha= 2/6)
	for (L2 in seq(1,12,1)){
	VGGFR(L1,L2,add=TRUE,col=c2[L2])}}
# Save and use the results 
res<-VGGFR(1.5,5.5)
res$kurt-res$oam/res$st.dev