afeddersen

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11 years, 64 days
I study psychology and economics with a very quantitative approach to each. I specialised on statistical methods, quantitative diagnostics, portfoio analysis and econometrics. Furthermore I am interested (and above that theoretically and empirlcally involved) in poker, chess and performing arts.

MaplePrimes Activity


These are replies submitted by afeddersen

@Alejandro Jakubi 

Thanks for your remark.

Until now I always had a constant "feeling" that there must be a difference between assume and assuming.

Now I know at least one aspect of their heterogeneousness.

Moreover it doesn´t help if I unassign mu and sigma after making assumptions in the first place.

E.g. I tried:

 

restart;
with(Statistics):
Y9 := RandomVariable(LogNormal(b, c)):
CRRA := t->((t)^(1-rho))/(1-rho):
interface(showassumed=0):
assume(t::real);
assume(0 < rho, rho <> 1):
assume(a::real, 0 < b, 0 < c):
assume(mu>0,sigma>0):
ExpectedValue(CRRA((Y9))):
g9 := simplify(%)=CRRA(s):
kCRRA9 := solve(g9, s, UseAssumptions);
g9:=solve({mu = Mean(Y9), sigma^2 = Variance(Y9)},{b,c}, Explicit)[1];
mu:='mu': sigma:='sigma':
gCRRA9:=simplify(normal(eval(kCRRA9,g9)));

 

which yields the same complicate result as above.

Moreover it doesn´t help if I unassign mu and sigma after making assumptions in the first place.

E.g. I tried:

 

restart;
with(Statistics):
Y9 := RandomVariable(LogNormal(b, c)):
CRRA := t->((t)^(1-rho))/(1-rho):
interface(showassumed=0):
assume(t::real);
assume(0 < rho, rho <> 1):
assume(a::real, 0 < b, 0 < c):
assume(mu>0,sigma>0):
ExpectedValue(CRRA((Y9))):
g9 := simplify(%)=CRRA(s):
kCRRA9 := solve(g9, s, UseAssumptions);
g9:=solve({mu = Mean(Y9), sigma^2 = Variance(Y9)},{b,c}, Explicit)[1];
mu:='mu': sigma:='sigma':
gCRRA9:=simplify(normal(eval(kCRRA9,g9)));

 

which yields the same complicate result as above.

So from your words I guess there is nothing I can do about it?

On the one hand I may need the assumptions, to make sure Maple will not complicate the result by misconceiving complex numbers or otherwise wrong domains.

On the other hand those very assumptions may complicate the result.

In a way this is very dissatisfying, for I need to simplify every single expression by hand, to make sure there is no way to simplify it any further, right?

So from your words I guess there is nothing I can do about it?

On the one hand I may need the assumptions, to make sure Maple will not complicate the result by misconceiving complex numbers or otherwise wrong domains.

On the other hand those very assumptions may complicate the result.

In a way this is very dissatisfying, for I need to simplify every single expression by hand, to make sure there is no way to simplify it any further, right?

What about

g5 := {b = sigma^2/mu, c = mu^2/sigma^2}; ?

This is what Maple suggests after

g5:=solve({mu = Mean(Y5), sigma^2 = Variance(Y5)},{b,c});

Shouldn´t I trust in this solution? Why should there be a need for independence, to solve this equation system?

Moreover I cannot see, why this should influence whether Maple substitutes c or not.

At least g5 defines what Maple should substitute for c.

 

What about

g5 := {b = sigma^2/mu, c = mu^2/sigma^2}; ?

This is what Maple suggests after

g5:=solve({mu = Mean(Y5), sigma^2 = Variance(Y5)},{b,c});

Shouldn´t I trust in this solution? Why should there be a need for independence, to solve this equation system?

Moreover I cannot see, why this should influence whether Maple substitutes c or not.

At least g5 defines what Maple should substitute for c.

 

Thank you for that.

Anyway, where can I read about the DirectSearch package?

I am not familiar with this package and I am not sure if I can follow in detail, what you did.

I tried ?DirectSearch, but recieved no matches.

Thank you for that.

Anyway, where can I read about the DirectSearch package?

I am not familiar with this package and I am not sure if I can follow in detail, what you did.

I tried ?DirectSearch, but recieved no matches.

That was easy but helped a lot! ;)

Thanks.

That was easy but helped a lot! ;)

Thanks.

Thanks for this idea.

Anyway, actually I was searching for a way to create an interactive plot with two dials for n and p resp.

I am not sure if this option was yet included in Maple13, which one you are using (IIRC).

But at least since Maple14 you can include "components" (e.g. dials, buttons, meters and the like) to change any predefined parameter and contemporaneously watch the consequence of that changes on the plot.

Thanks for this idea.

Anyway, actually I was searching for a way to create an interactive plot with two dials for n and p resp.

I am not sure if this option was yet included in Maple13, which one you are using (IIRC).

But at least since Maple14 you can include "components" (e.g. dials, buttons, meters and the like) to change any predefined parameter and contemporaneously watch the consequence of that changes on the plot.

In my version it sais:

mu*exp(-(1/2)*rho*(ln(mu^2+sigma2)+2*ln(1/mu)))

for s1, while it displays s2 as shown by you above.

This is quite puzzling.

 

In my version it sais:

mu*exp(-(1/2)*rho*(ln(mu^2+sigma2)+2*ln(1/mu)))

for s1, while it displays s2 as shown by you above.

This is quite puzzling.

 

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