[R] Fitting of lognormal distribution to lower tail experimental data

[Göran Broström]

On Fri, Jan 16, 2009 at 3:31 PM, Mattias Brännström
<Mattias.Brannstrom at tt.luth.se> wrote:
> Thank you, David!
>
> I agree and apprechiate your analysis, which definitely will influence my
> analysis of this data, but still I would like you to disregard from it(!)
>
> The standard routine in the field is, beyond my control, to assume
> lognormal distribution to achieve comparable results also with other
> materials (comparison is made on COV). For that reason I have to use it,
> even if it is not statistically defendable for this particular data.
>
> So, if I rephrase the question to be (more general):
> How would you fit a lognormal distribution to the lower 10% tail of the
> data (assuming it was lognormal)? What functions to use?

Mattias, it is not clear (to me) what you mean by "fit a lognormal
distribution to the 10%-lower tail of the attached data" (and what is
COV?). However, a guess is that you really mean what you say, so I
tried to right-censor your data at the 10% quantile (33.4134, Type I
censoring) and fit the resulting data to a lognormal distribution. The
fit was fairly good, as can be seen by comparing the fitted cumulative
hazard function to the corresponding non-parametric one (the
Nelson-Aalen estimator):

> cc <- read.table(....
> v1 <- ifelse(cc$V1 <= 33.4134, cc$V1, 33.4134)
> event <-  as.numeric(cc$V1 <= 33.4134)
> library(eha)
Loading required package: survival
Loading required package: splines
> fit.ln <- phreg(Surv(v1, event) ~ 1, dist = "lognormal")
> fit.cox <- coxreg(Surv(v1, event) ~ 1)
> check.dist(fit.cox, fit.ln)# Gives you a plot
> summary(fit.ln)
Call:
phreg(formula = Surv(v1, event) ~ 1, dist = "lognormal")

Covariate                Coef Exp(Coef)  se(Coef)    Wald p
log(scale)              3.943    51.597     0.053     0.000
log(shape)             1.089      2.970     0.101     0.000

Events                    70
Total time at risk         22998
Max. log. likelihood      -401.38

Is this maybe what you are looking for?

HTH (!)

Göran

> Best regards,
> Mattias
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>



-- 
Göran Broström