# GGFR: Vianelli density In pvrank: Rank Correlations

## Description

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

## Usage

 `1` ```VGGFR(L1, L2, add=FALSE, lwd=2, lty=5, col="blue", ylim=c(0,1), Main="", 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. `ylim` numeric vectors of length 2, giving the y coordinates ranges. `Main` a string describing the graph. `np` number of points to be plotted.

## Details

The VGGFR density is given by

f(r;λ_1,λ_2)=λ_1(1-|r|^{λ_2})^{λ_1}/[2B(1/λ_1,λ_2+1)]

where λ_1,λ_2>0 and B() is the beta function.

## Value

The value returned is a list contaning:

 `st.dev` standard deviation `kurt` kurtosis `oam` ordinate at the mode

## Note

If you want to use the output from VGGFR save the result and then select from the list the value(s) needed.

## Author(s)

Agostino Tarsitano and Ilaria Lucrezia Amerise

## References

Tarsitano, A. and Amerise, I. L. (2016). "Modelling of the null distribution of rank correlations". Submitted.

Vianelli, S. (1968). "Sulle curve normali di ordine \$r\$ per intervalli finiti delle variabili statistiche". Annali della Facolt\‘a di Economia e Commercio dell’Universit\'a di Palermo, 2.

Vianelli, S. (1983). "The family of normal and lognormal distributions of order r". Metron, 41, 3-10.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43``` ``` # Density curve of a VGGFR model VGGFR(2, 12, add=FALSE, lwd=2, lty=5, col="darkgreen", ylim=c(0,2), Main="", np=201) ##### # a<-ranktes(0.5, 28, "r4", "vg",FALSE, "two", FALSE) b<-VGGFR(a\$Lambda, add = FALSE, lwd = 2, lty = 5, col = "blue", ylim=c(0,2.5),np = 201) ##### # # Lambert's semicircular distribution of errors (1760,1765). # Given a probability distribution, the value with the higher probability density is # deemed to be more probable than the value with the lower probability density. # VGGFR(2,0.5,col="red",ylim=c(0,0.75),Main="Lambert's distribution of errors") # ##### # Pearson type II used as an approximation to the null distribution of the Fisher-Yates # rank correlation. Fieller, E. C. and Pearson, E. S. (1961). Tests for rank correlation # coefficients: II. Biometrika, 48, 29-40. n<-10 VGGFR(2, (n-4)/2, add=FALSE, lwd=2, lty=5, col="magenta2", ylim=c(0,1.1), Main="", np=201) abline(h=0);abline(v=0,lty=2,lwd=2,col="pink2") ##### # # Save and use the results res<-VGGFR(1.5,5.5,add = FALSE, lwd = 2, lty = 1, col = "blue", ylim=c(0,2.5),np = 201) res\$kurt-res\$oam/res\$st.dev ##### # # A family of symmetrical beta densities VGGFR(2,1,col="black",ylim=c(0,1.4),Main="Symmetrical beta densities") La<-seq(1,6,0.5) for (L1 in La){VGGFR(2,L1,add=TRUE, lwd = 1, lty = 1, col=gray(L1/6))} ##### # # A family of GGFR curves VGGFR(1,2, lwd = 1, lty = 1,col="black",ylim=c(0,5)) 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, lwd = 1, lty = 1, col=c2[L2]) }} ```

pvrank documentation built on May 17, 2018, 9:03 a.m.