Description Usage Arguments Details Value Author(s) References See Also Examples
Returns ρ_p, used in the calculation of the strong asymetry measure η(X).
1 | Rho.p.exact(xin, p.param, dist, p1=0, p2=1)
|
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. |
Implements the quantity:
\frac{ 2√{3}}{p} \frac{-\int_{-∞}^{ξ_p} f^2(x)F(x)\,dx - \frac{p}{2}\int_{-∞}^{ξ_p} f^2(x)\,dx}{ ≤ft \{ p\int_{-∞}^{ξ_p} f^3(x)\,dx-(\int_{-∞}^{ξ_p} f^2(x)\,dx)^2 \right \}^{1/2} }
defined on page 6 Patil, Bagkavos and Wood, see also (4) in Bagkavos, Patil and Wood . This implementation uses exact calculation of the functionals in the definition of ρ_p.
Returns a scalar, the exact value of ρ_p.
Dimitrios Bagkavos and Lucia Gamez Gallardo
R implementation and documentation: Dimitrios Bagkavos <dimitrios.bagkavos@gmail.com> , Lucia Gamez Gallardo <gamezgallardolucia@gmail.com>
Rho.p,Rhostar.p, Rhostar.p.exact
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 | 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
Rho.p.exact(xout,param,selected.r,shape,scale) # calculate Rho.p.exact
#-0.06665222 # 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
Rho.p.exact(xout,param,selected.r2,mean,sd) # calculate Rho.p.exact
#-0.2384271 # 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
Rho.p.exact(xout,param,selected.r3,location,scale) # calculate Rho.p.exact
#-0.02340374 # returns the result
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