# [R] Help : stablereg parameter interpretation

pfm401@lineone.net pfm401 at lineone.net
Tue Mar 25 13:33:08 CET 2003

```Dear all,

I am having difficulty interpreting the parameter estimates from the stablereg
function. Specifically I am trying to keep things simple to start with by
using stablereg to fit a normal distribution to a simulated data set from
that distribution (in order to understand the way that stablereg reports
parameter estimates). I cannot work out the scale on which the dispersion
parameter (some function of the standard deviation if the data are normal)
is reported. The location parameter i.e. the mean is obvious.

For example:

set.seed(1234)
# Simulate normal data with mean 5 and sd 2 using rstable> normal5.2<-rstable(10000,loc=5,disp=2/sqrt(2),skew=0,tail=2)
mean(normal5.2)
 5.010073
sd(normal5.2)
 2.005362

# summary(lm(normal5.2~1)) yields similar results

fittest<-stablereg(y=normal5.2,loc=~1,disp=~1,iloc=5,idisp=2/sqrt(2),iskew=0,itail=2,oskew=F,otail=F)
# Normal model, as skew=0 and tail=2

yields :

Call:
stablereg(y = normal5.2, loc = ~1, disp = ~1, iloc = 5, idisp = 2/sqrt(2),

iskew = 0, itail = 2, oskew = F, otail = F)

-Log likelihood              21498.69
No. of obs                   10000
No. of estimated parameters  2
No. of parameters            4
Degrees of freedom           9998
AIC                          21500.69
Iterations                   6

Location parameters
~1
estimate       se
(Intercept)     5.015  0.02011

Dispersion parameters
estimate        se
1    0.2888  0.008753

Correlations:
1         2
1  1.000000 -0.001761
2 -0.001761  1.000000

so that 5.015 is indeed the (approx.) mean. As dispersion uses a log link
function and disp=sd/sqrt(2) for the normal (I think!) I tried
sqrt(2)*exp(0.2888)
which gives 1.887727
and 95% confidence limits at sqrt(2)*exp(0.2888+-1.96*0.008753)
i.e. (1.854968,1.921065)

Without going into more detail I have tried this for different parameter
values and simulations and cannot resolve the dispersion parameter to the
standard deviation. Clearly I am missing something!!

Any help is much appreciated.