pwmRC). The $$\lambda^B_1 = \xi + \alpha m_1 \mbox{,}$$ $$\lambda^B_2 = \alpha (m_1 - m_2) \mbox{,}$$ $$\lambda^B_3 = \alpha (m_1 - 3m_2 + 2m_3)\mbox{,}$$ $$\lambda^B_4 = \alpha (m_1 - 6m_2 + 10m_3 - 5m_4)\mbox{, and}$$ $$\lambda^B_5 = \alpha (m_1 - 10m_2 + 30m_3 - 35m_4 + 14m_5)\mbox{,}$$
RC in the function name is to denote Right-tail Censoring.pwm2lmom from B-type Probability-Weighted Moments from pwmRC.}
optimize function. For the L-moments of the distribution to be valid $\kappa > -1$.}
optimize function. Hopefully, a large enough default is chosen for real-world data sets.}
lmom be checked for validity using the are.lmom.valid function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the $\tau_4$ and $\tau_3$ inequality). However, for some circumstances or large simulation exercises then one might want to bypass this check.}
list is returned.
gpa.}
list returned by the optimize function.}
optimize function is used to numerically solve for the shape parameter $\kappa$. No test or evaluation is made on the quality of the minimization. Users should concults the contents of the optim portion of the returned list. Finally, this function should return the same parameters if $\zeta=1$ as the pargpa function.
Hosking, J.R.M., 1995, The use of L-moments in the analysis of censored data,
in Recent Advances in Life-Testing and Reliability, edited by N. Balakrishnan,
chapter 29, CRC Press, Boca Raton, Fla., pp. 546--560.
[object Object]
lmomgpa, lmomgpaRC, pargpa,
cdfgpa, quagpa
pwm2 <- pwmRC(fakedata,threshold=threshold) # compute censored PWMs typeBpwm <- pwm2$Bbetas # the B-type PWMs zeta <- pwm2$zeta # the censoring fraction
cenpara <- pargpaRC(pwm2lmom(typeBpwm),zeta=zeta) # Estimated parameters F <- nonexceeds() # nonexceedance probabilities for plotting purposes
# Visualize some data plot( F,quagpa(F,para),type='l', lwd=3) # The true distribution lines( F,quagpa(F,estpara),col=3) # Green estimated in the ordinary fashion lines(F,quagpa(F,cenpara),col=2) # Red, consider that the data is censored # now add in what the drawn sample looks like. PP <- pp(fakedata) # plotting positions of the data points(PP,sort(fakedata)) # sorting is needed! # Interpretation. You should see that the red line more closely matches # the heavy black line. The green line should be deflected to the right # and pass through the values equal to the threshold, which reflects the # much smaller L-skew of the ordinary L-moments compared to the type-B # L-moments.
# Assertion, given some PWMs or L-moments, if zeta=1 then the parameter
# estimates must be identifical. The following provides a demonstration.
para1 <- pargpaRC(pwm2lmom(typeBpwm),zeta=1)
para2 <- pargpa(pwm2lmom(typeBpwm))
str(para1)
str(para2)