Description Usage Arguments Details Value Author(s) References See Also Examples
Estimates ρ_p^*, used in the calculation of the strong asymetry measure η(X).
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_{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). Estimation of the p.d.f. and c.d.f. functions is currently performed by maximum likelihood as e.g. kernel estimates inherit large amount of variance to ρ_p^*.
Returns a scalar, the 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.exact, Rho.p.exact
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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(xout,param,selected.r,shape,scale) # calculate Rhostar.p
#-0.08936363 # 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(xout,param,selected.r2,mean,sd) # calculate Rhostar.p
#-0.02302223 # 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(xout,param,selected.r3,location,scale) # calculate Rhostar.p
#0.02043852 # returns the result
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