# [R] low sigma in lognormal fit of gamlss

RdR richard.derozario at gmail.com
Tue Nov 1 04:34:46 CET 2011

```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 Coefficients:
Estimate  Std. Error  t value  Pr(>|t|)
(Intercept)     9.947     0.06305    157.8         0

-------------------------------------------------------------------
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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```