[R] Fitting weibull, exponential and lognormal distributions to left-truncated data.

[Gough Lauren]

Hi,

Thank you very much for your reply. This seems to be working OK when
fitting weibull and lognormal distributions.  However, fitdistr now
requires me to include start values:

> ltwei<-function(x,shape,scale,log=FALSE){
+ dweibull(x,shape,scale,log)/pweibull(1,shape,scale,lower=FALSE)
+ }
> ltweifit<-fitdistr(x,ltwei) # x is observed data
Error in fitdistr(x, ltwei) : 'start' must be a named list
> ltweifit<-fitdistr(x,ltwei,start=list(shape=0.5,scale=0.5))
There were 34 warnings (use warnings() to see them)
> ltweifit
      shape         scale   
   1.11108278   13.00703630 
 ( 0.01936651) ( 0.42897340)

Is there anyway I can fit to truncated data without having to name start
values?  Alternatively, is there any recommended technique for choosing
sensible start values?

Further, when I try to fit an exponential distribution I get an error
message:

>ltexp<-function(x,rate,log=FALSE){
+ dexp(x,rate,log)/pexp(1,rate,lower=FALSE)
+ }
> ltexpfit<-fitdistr(x,ltexp)
Error in fitdistr(x, ltexp) : 'start' must be a named list
> ltexpfit<-fitdistr(x,ltexp,start=list(0.1))
Warning message:
In optim(x = c(2.541609, 1.436143, 4.600524, 6.437174, 2.84974,  :
  one-diml optimization by Nelder-Mead is unreliable: use optimize
> ltexpfit
Error in dn[[2]] : subscript out of bounds

This error message seems to occur regardless of the start value used.
Do you know why this is?  

Sorry to pester you again, and apologies if I am asking silly questions
- my knowledge of R and probability distributions (except the normal!)
are rather limited!

Best wishes

Lauren 

-----Original Message-----
From: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk] 
Sent: 07 October 2008 12:25
To: Richard.Cotton at hsl.gov.uk
Cc: Gough Lauren; vito muggeo; r-help at r-project.org
Subject: Re: [R] Fitting weibull, exponential and lognormal
distributions to left-truncated data.

On Tue, 7 Oct 2008, Richard.Cotton at hsl.gov.uk wrote:

>>> I have several datasets, all left-truncated at x=1, that I am
> attempting
>>> to fit distributions to (lognormal, weibull and exponential).  I had

>>> been using fitdistr in the MASS package as follows:
>
>> A possible solution is to use the survreg() in the survival package 
>> without specifying the covariates, i.e.
>>
>> library(survival)
>> survreg(Surv(..)~1, dist="weibull")
>>
>> where Surv(..) accepts information about "times", 
>> censoring/truncation variables and dist allows to specify alternative
distributions.
>> See ?Surv e ?survreg
>
> The survival package is mostly targeted at right-censored data.  The 
> NADA package provides wrappers for many of the survival routines so 
> they work with left-censored data.

Left-censoring and left-truncation are not the same thing.  With
left-censoring you see that you had observations < 1, and with
left-truncation you do not (at least how the terms are usually applied: 
occasionally the meanings are reversed).

For left-truncation it is relatively easy, e.g.

ltwei <- function(x, shape, scale = 1, log = FALSE)
     dweibull(x, shape, scale, log)/pweibull(1, shape, scale,
lower=FALSE)

and use this in fitdistr.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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