Description Usage Arguments Details Value Author(s) References See Also Examples
View source: R/d_rsize_Weibull.R
Calculates the density of the r-size biased Weibull distribution.
1 | d_rsize_Weibull(x,TRpar,r)
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x |
Grid points where the functional is being calculated. |
TRpar |
A vector of length 2, containing the shape and scale parameters of the distribution. |
r |
The size (order) of the distribution. The special cases r=1,2,3 correspond to length, area, volume biased samples respectively and are the most frequently encountered in practice. The case r=0 corresponds to random samples from the Weibull distribution. |
The r-size density of the observed biased sample X_1, …, X_n is defined by
f_r(x; θ)=\frac{x^r f(x; θ)}{E(X^r)}
where f(x; θ) is the density of the Weibull distribution and θ the vector of the shape and scale parameters of the distribution.
A vector of length equal to the length of x.
Polychronis Economou
R implementation and documentation: Polychronis Economou <peconom@upatras.gr>
Economou et. al. (2021). Hypothesis testing for the population mean and variance based on r-size biased samples, under review.
p_rsize_Weibull
, r_rsize_Weibull
1 2 3 4 5 6 7 8 9 10 | # example of r-size Weibull distribution, r=0,1,2
x<- seq(0, 10, length=50)
dens.0.size<-d_rsize_Weibull(x,c(2,3),0)
dens.1.size<-d_rsize_Weibull(x,c(2,3),1)
dens.2.size<-d_rsize_Weibull(x,c(2,3),2)
plot(x, dens.0.size, type="l", ylab="r-denisty")
lines(x, dens.1.size, col=2)
lines(x, dens.2.size, col=3)
legend("topright",legend=c("r= 0","r= 1","r= 2"),
col=c("black","red","green"),lty=c(1,1,1))
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