[R] threshold distribution

[J. R. M. Hosking]

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