Rhostar.p.exact {asymmetry.measures} R Documentation

## Calculates the exact value of ρ_p^*, used in the implementation of the strong asymmetry measure η(X).

### Description

Returns ρ_p^*, used in the calculation of the strong asymetry measure η(X).

### Usage

  Rhostar.p.exact(xin, p.param, dist, p1, p2)


### Arguments

 xin A vector of data points - the available sample. p.param A parameter with the value greater than or equal to 1/2 and less than 1. dist Character string, specifies selected distribution function. p1 A scalar. Parameter 1 (vector or object) of the selected distribution. p2 A scalar. Parameter 2 (vector or object) of the selected distribution.

### Details

Implements the quantity

\frac{ 2√{3}}{p} \frac{-\int_{ξ_{1-p}}^{∞}{f^2(x)(1-F(x))\,dx}+\frac{p}{2}\int_{ξ_{1-p}}^{∞} f^2(x)\,dx}{ ≤ft \{ p\int_{ξ_{1-p}}^{∞}f^3(x)\,dx-(\int_{ξ_{1-p}}^{∞}f^2(x)\,dx)^2 \right \}^{1/2} }

defined on page 6 Patil, Bagkavos and Wood (2014), see also (5) in Bagkavos, Patil and Wood (2016). This implementation uses exact calculation of the functionals in the definition of ρ_p^*.

### Value

Returns a scalar, the exact value of ρ_p^*.

### Author(s)

Dimitrios Bagkavos and Lucia Gamez Gallardo

R implementation and documentation: Dimitrios Bagkavos <dimitrios.bagkavos@gmail.com> , Lucia Gamez Gallardo <gamezgallardolucia@gmail.com>

### References

Rho.p, Rhostar.p, Rho.p.exact

### Examples

set.seed(1234)

selected.r <- "weib" #select Weibull as the distribution
shape <- 1 # specify shape parameter
scale <- 1  # specify scale parameter
n <- 100    # specify sample size
param <- 0.9 # specify parameter
xout<-r.sample(n,selected.r,shape,scale) # specify sample
Rhostar.p.exact(xout,param,selected.r,shape,scale)  # calculate Rhostar.p.exact
#-0.05206678  # returns the result

selected.r2 <- "norm" #select Normal as the distribution
n <- 100    # specify sample size
mean <- 0 # specify the mean
sd <- 1 # specify the variance
param <- 0.9 # specify parameter
xout <-r.sample(n,selected.r2,mean,sd) # specify sample
Rhostar.p.exact(xout,param,selected.r2,mean,sd) # calculate Rhostar.p.exact
#-0.008687447 # returns the result

selected.r3 <- "cauchy" #select Cauchy as the distribution
n <- 100    # specify sample size
location <- 0 # specify the location parameter
scale <- 1 # specify the scale parameter
param <- 0.9 # specify parameter
xout<-r.sample(n,selected.r3,location,scale) # specify sample
Rhostar.p.exact(xout,param,selected.r3,location,scale) # calculate Rhostar.p.exact
#0.0280602  # returns the result


[Package asymmetry.measures version 0.2 Index]