Consider the following expression:

sCARA4 := -ln(-(mu/sigma^2)^(mu^2/(mu-sigma^2))*(sigma^2/mu)^(mu^2/(mu-sigma^2))+(sigma^2/mu)^(mu^2/(mu-sigma^2))*((exp(phi)*sigma^2+mu-sigma^2)*exp(-phi)/sigma^2)^(mu^2/(mu-sigma^2))+1)/phi;

Now try to find out whether the first derivative to mu is positive for all positive mu, phi and sigma, except for some rare exceptions (e.g. sigma^2=mu).

diff(%,mu);

Since 'is' is not a satisfying option, I used 'Explore'...

To my mind I did all the necessary assumptions, to avoid that the summand will become singular when calculating the expected value.

What did I do wrong?

Here´s the code:

with(Statistics):
interface(showassumed=0):
assume(t::posint):
assume(x::posint):
assume(0 < q, q < 1):
X1 := RandomVariable(Geometric(q)):
DARA := t->log(t):
ExpectedValue(DARA(X1));

In the following code Maple simplifies the last expression different, based on whether assume(mu::real, sigma>0) is set or not.

The point is, that the assumptions got -to my mind- nothing to do with the displayed results.

Why does Maple do such weird things?

Here is the code. The last output is different based on whether the '#' before assume(mu::real,sigma>0): is set or not:

restart;
with(Statistics):
Y9 := RandomVariable(LogNormal(b, c)):

I discovered, that Maple did substitute every single parameter but c!

Anyway, when I isolate the problem and do not assume anything for mu and sigma, the problem does not occur.

Therefore I print here the complete relevant code.

Is there a way to "convince" Maple to do those trivial substitutions of c also, without seperating each problematical expression?

Here is the code:

restart;
with(Statistics):

#Definitions and assumptions

I tried to find out whether the expression

g1:=2*mu*(phi+ln(mu/(exp(phi)*sigma2-sigma2+mu)))/((-sigma2+mu)*phi)+mu*(1/(exp(phi)*sigma2-sigma2+mu)-mu/(exp(phi)*sigma2-sigma2+mu)^2)*(exp(phi)*sigma2-sigma2+mu)/((-sigma2+mu)*phi)-mu^2*(phi+ln(mu/(exp(phi)*sigma2-sigma2+mu)))/((-sigma2+mu)^2*phi);

is positive under the given assumptions:

         
is(signum(g1)=1) assuming mu>0, sigma2>0, phi>0, sigma2<>mu;