threshold distribution
Abelian wrote:
Dear ALL
I have a list of data below
0.80010 0.72299 0.69893 0.99597 0.89200 0.69312 0.73613 1.13559
0.85009 0.85804 0.73324 1.04826 0.84002
1.76330 0.71980 0.89416 0.89450 0.98670 0.83571 0.73833 0.66549
0.93641 0.80418 0.95285 0.76876 0.82588
1.09394 1.00195 1.14976 0.80008 1.11947 1.09484 0.81494 0.68696
0.82364 0.84390 0.71402 0.80293 1.02873
all of them are ninty.
Nowaday, i try to find a distribution to fit those data.
Firstly, I normalize the data, i.e.. (x-mean(X))/(sd(X))
i utilize the SAS to fit my data. Then i obtain the result below
##-------------------------------------------------------------------------------------------------------------
Parameters for Lognormal
Distribution
Parameter Symbol
Estimate
Threshold Theta
-1.51062
Scale
Zeta 0.237283
Shape Sigma
0.593481
Mean
0.001321
Std
Dev 0.982435
##-------------------------------------------------------------------------------------------------------------------
however, i confuse about the threshold parameter..
How to get it? Does it be able to be calculated by R?
Function pelln3 in package lmom will estimate all 3 parameters
of the 3-parameter lognormal distribution, including the threshold ...
> x <- scan(textConnection("
+ 0.80010 0.72299 0.69893 0.99597 0.89200 0.69312 0.73613 1.13559
+ 0.85009 0.85804 0.73324 1.04826 0.84002
+ 1.76330 0.71980 0.89416 0.89450 0.98670 0.83571 0.73833 0.66549
+ 0.93641 0.80418 0.95285 0.76876 0.82588
+ 1.09394 1.00195 1.14976 0.80008 1.11947 1.09484 0.81494 0.68696
+ 0.82364 0.84390 0.71402 0.80293 1.02873
+ "))
Read 39 items
>
> y <- (x-mean(x))/sd(x)
>
> library(lmom)
> pelln3(samlmu(y))
zeta mu sigma
-1.5362134 0.2554631 0.5896735
J. R. M. Hosking