lmomco (version 1.7.3)

paremu: Estimate the Parameters of the Eta-Mu Distribution

Description

This function estimates the parameters ($\eta$ and $\alpha$) of the Eta-Mu ($\eta:\mu$) distribution given the L-moments of the data in an L-moment object such as that returned bylmom.ub. The relations between distribution parameters and L-moments are complex.

Usage

paremu(lmom, checklmom=TRUE, checkbounds=TRUE,
         alsofitT3=FALSE, alsofitT3T4=FALSE, alsofitT3T4T5=TRUE,
         justfitT3T4=FALSE, boundary.tolerance=0.001,
         verbose=FALSE, trackoptim=TRUE)

Arguments

lmom

A L-moment object created by lmom.ub or pwm2lmom.

checklmom

Should the 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 $\tau_3$ ineq

checkbounds

Should the L-skew and L-kurtosis boundaries of the distribution be checked.

alsofitT3

Logical when true will add the error term $(\hat\tau_3 - \tau_3)^2$ to the sum of square errors for the mean and L-CV.

alsofitT3T4

Logical when true will add the error term $(\hat\tau_3 - \tau_3)^2 + (\hat\tau_4 - \tau_4)^2$ to the sum of square errors for the mean and L-CV.

alsofitT3T4T5

Logical when true will add the error term $(\hat\tau_3 - \tau_3)^2 + (\hat\tau_4 - \tau_4)^2 + (\hat\tau_5 - \tau_5)^2$ to the sum of square errors for the mean and L-CV.

justfitT3T4

Logical when true will only consider the sum of squares errors for L-skew and L-kurtosis as mathematically shown for alsofitT3T4.

boundary.tolerance

A fudge number to help guide how how to the boundaries an arbitrary list of $\tau_3$ and $\tau_4$ can be to consider them formally in or out of the attainable ${\tau_3, \tau_4}$ domain.

verbose

A logical to control a level of diagnostic output.

trackoptim

A logical to control specific messaging through each iteration of the objective function.

Value

• An R list is returned.
• type
  The type of distribution: emu.
• para
  The parameters of the distribution.
• source
  The source of the parameters: paremu.

References

Yacoub, M.D., 2007, The kappa-mu distribution and the eta-mu distribution: IEEE Antennas and Propagation Magazine, v. 49, no. 1, pp. 68--81

See Also

lmom.ub, lmomemu, cdfemu, quaemu

Examples

par1 <- vec2par(c(.3, 2.15), type="emu")
   lmr1 <- lmomemu(par1, nmom=4)
   par2.1 <- paremu(lmr1, alsofitT3=FALSE, verbose=TRUE, trackoptim=TRUE)
   par2.1$para # correct parameters not found: eta=0.889 mu=3.54
   par2.2 <- paremu(lmr1, alsofitT3=TRUE, verbose=TRUE, trackoptim=TRUE)
   par2.2$para # correct parameters not found: eta=0.9063 mu=3.607
   par2.3 <- paremu(lmr1, alsofitT3T4=TRUE,  verbose=TRUE, trackoptim=TRUE)
   par2.3$para # correct parameters not found: eta=0.910 mu=3.62
   par2.4 <- paremu(lmr1, justfitT3T4=TRUE,  verbose=TRUE, trackoptim=TRUE)
   par2.4$para # correct parameters not found: eta=0.559 mu=3.69

   x <- seq(0,3,by=.01)
   plot(x,  pdfemu(x, par1), type="l", lwd=6, col=8, ylim=c(0,2))
   lines(x, pdfemu(x, par2.1), col=2, lwd=2, lty=2)
   lines(x, pdfemu(x, par2.2), col=4)
   lines(x, pdfemu(x, par2.3), col=3, lty=3, lwd=2)
   lines(x, pdfemu(x, par2.4), col=5, lty=2, lwd=2)