quarevgum {lmomco} | R Documentation |
This function computes the quantiles of the Reverse Gumbel distribution given
parameters (xi and α) of the distribution computed by
parrevgum
.
The quantile function of the distribution is
x(F) = xi + αlog(-log(1-F)) mbox{,}
where x(F) is the quantile for nonexceedance probability F,
xi is a location parameter, and α is a scale parameter. Notice that the function has some sign differences and uses the complement of F compared to the Gumbel quantile function in quagum
.
quarevgum(f, para)
f |
Nonexceedance probability (0 <= F <= 1). |
para |
The parameters from parrevgum or similar. |
Quantile value for nonexceedance probability F.
W.H. Asquith
Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.
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.
# See p. 553 of Hosking (1995) # Data listed in Hosking (1995, table 29.3, p. 553) D <- c(-2.982, -2.849, -2.546, -2.350, -1.983, -1.492, -1.443, -1.394, -1.386, -1.269, -1.195, -1.174, -0.854, -0.620, -0.576, -0.548, -0.247, -0.195, -0.056, -0.013, 0.006, 0.033, 0.037, 0.046, 0.084, 0.221, 0.245, 0.296) D <- c(D,rep(.2960001,40-28)) # 28 values, but Hosking mentions 40 values in total z <- pwmRC(D,threshold=.2960001) str(z) # Hosking reports B-type L-moments for this sample are # lamB1 = -.516 and lamB2 = 0.523 btypelmoms <- pwm2lmom(z$Bbetas) # My version of R reports lamB1 = -0.5162 and lamB2 = 0.5218 str(btypelmoms) rg.pars <- parrevgum(btypelmoms,z$zeta) str(rg.pars) # Hosking reports xi = 0.1636 and alpha = 0.9252 for the sample # My version of R reports xi = 0.1635 and alpha = 0.9254 F <- nonexceeds() PP <- pp(D) # plotting positions of the data plot(PP,sort(D),ylim=range(quarevgum(F,rg.pars))) lines(F,quarevgum(F,rg.pars)) # In the plot notice how the data flat lines at the censoring level, but the # distribution continues on. Neat.