[R] low sigma in lognormal fit of gamlss

[RdR]

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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