Fitting of lognormal distribution to lower tail experimental data

On Fri, Jan 16, 2009 at 3:31 PM, Mattias Br?nnstr?m

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 (!)

G?ran

Best regards,
Mattias

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G?ran Brostr?m