Log-Normal: Means and Variances

[Stratocaster]

I am posting to ask for help/verification regarding two relatively simple
questions I have regarding Log Normal Random Variables. I believe my work
is correct, but I would feel much more confident if someone else (who is
more experienced with this) would confirm my belief. I am really just
looking for a "yeah, that looks right" or, "Oh no you didn't". Thanks

I am concerned with calculations of means and variances when either the X or
Y term are modified by a constant (which I will denote with 'c'). i.e.

X+c = Ln(Y) AND X = Ln(Y + c)

(I suppose it must be said): Where X and Y are Random Variables and X is
normally distributed with parameters 'mu' and 'sigma'.

When I refer to "the regular expression for the mean/variance", I am
refering to:
where X = Ln(Y)
E(Y) = e^[mu+(sigma^2)/2]
V(Y) = (e^[2*mu+sigma^2])*([e^sigma^2]-1)

Case I: X+c = Ln(Y)

E(Y) = (e^c)*(regular expression for the mean)
V(Y) = (e^c^2)*(regular expression for the variance)

Case II: X = Ln(Y+c)

E(Y) = (regular expression for the mean) - c
V(Y) = (regular expression for the variance)

I would supply my work, but it seems trivial, almost to trivial (which is my
concern)... I will post it if you feel it is necessary.
Thanks for taking the time to help me.

[Ray Koopman]

I parse e^c^2 as e^(c^2). For the case I variance,
I would write the multiplier as (e^c)^2 = e^(2c).

[Stratocaster]

"Ray Koopman" <koo...@sfu.ca> wrote in message
news:1194776437....@t8g2000prg.googlegroups.com...

This is another interesting topic to me. I usually interpret (e^c^2) as
(e^c)^2, but will agree that (e^c^2) is ambiguous (after all, you interpret
it differently from me). Regardless, thanks for taking the time to help me.

[elodie....@gmail.com]

On Nov 11, 3:02 pm, "Stratocaster" <sto...@verizon.net> wrote:
> "Ray Koopman" <koop...@sfu.ca> wrote in message

For case 2,
I would argue that you are defining a location family of Y. In
location families, the expectation if expectation of the Y (the
reference) plus the location parameter (-c). And the variance does not
change. Just my two cents.

[Stratocaster]

<elodie....@gmail.com> wrote in message

> > > > Case I: X+c = Ln(Y)
> >
> > > > E(Y) = (e^c)*(regular expression for the mean)
> > > > V(Y) = (e^c^2)*(regular expression for the variance)
> >
> > > > Case II: X = Ln(Y+c)
> >
> > > > E(Y) = (regular expression for the mean) - c
> > > > V(Y) = (regular expression for the variance)

> For case 2,

> I would argue that you are defining a location family of Y. In
> location families, the expectation if expectation of the Y (the
> reference) plus the location parameter (-c). And the variance does not
> change. Just my two cents.

I had never heard of a location family (or location-scale family) before.
Thanks for pointing this topic out to me. Pretty neat stuff.