R help - Nov 2011 - low sigma in lognormal fit of gamlss

Hi,

I'm playing around with gamlss and don't entirely understand the sigma
result from an attempted lognormal fit.

In the example below, I've created lognormal data with mu=10 and sigma=2. 
When I try a gamlss fit, I get an estimated mu=9.947 and sigma=0.69

The mu estimate seems in the ballpark, but sigma is very low. I get similar
results on repeated trials and with Normal and standard normal
distributions.  How should I understand sigma in these results?

cheers,
RdR


######### Example  #########
# enable reproduction
set.seed(1234)

# create some lognormal data
X <- rlnorm(1000,meanlog=10,sdlog=2)

# try gamlss fit
gLNO <- gamlss(X~1,family=LNO)

summary(gLNO)

*******************************************************************
Family:  c("LNO", "Box-Cox") 

Call:  gamlss(formula = X ~ 1, family = LNO) 

Fitting method: RS() 

-------------------------------------------------------------------
Mu link function:  identity
Mu Coefficients:
             Estimate  Std. Error  t value  Pr(>|t|)
(Intercept)     9.947     0.06305    157.8         0

-------------------------------------------------------------------
Sigma link function:  log
Sigma Coefficients:
             Estimate  Std. Error  t value
(Intercept)      0.69     0.02236    30.86
              Pr(>|t|)
(Intercept)  2.19e-147

-------------------------------------------------------------------
No. of observations in the fit:  1000 
Degrees of Freedom for the fit:  2
      Residual Deg. of Freedom:  998 
                      at cycle:  2 
 
Global Deviance:     24111.45 
            AIC:     24115.45 
            SBC:     24125.27 
*******************************************************************
Warning message:
In summary.gamlss(gLNO) :
  summary: vcov has failed, option qr is used instead


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Actually, I think I've spotted it: the link function for sigma is
"log" and
exp(0.69) is nearly 2 -- the original sigma

-RdR

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