mmcdara

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These are questions asked by mmcdara

Hi, 

I can't find a unique way to define a mixture of two random variables that enables at the same time to compute its PDF and generate a sample.
In the attached file you will find two methods :

  1. the first one is the most formal and only CAS are supposed to be able to allow its implementation:
     it enables computing the PDF and the CDF (trivial) but fails to generate a sample.
    (PS : in a first attempt I had defined only the PDF, which should have been enough for method=envelope does work... ... at my opinion)
     
  2. the second method is the one one would use in non CAS languages (for instance Matlab, R, ...). It enables generating a sample (of course) but fails to compute the PDF (which is not very surprising).

So my question: does anyone here would have some suggestions to make one these two methods capable to compute both the PDF (eventually the CDF) and generate samples ?

PS: still have this kind of problems (tomleslie suggested months ago that using interface(rtablesize=10) could help but it's not the case here)
Maple Worksheet - Error
Failed to load the worksheet /maplenet/convert/Mixture_of_random_variables.mw .

 

Download Mixture_of_random_variables.mw

 

Hi 

I got, a bit by mistake, a weird result that seems to come from the way "Maple" manipulates infinity (please have a look at the results below)
I couldn't find a correct explanation to these results in the help pages dedicated to infinity or evaluation.

Could anyone explain me why, in some circumstances, 'infinity' seems to be a name (for instance infinity*Pi; does not return  infinity but infiniy/Pi).
Thanks in advance

 

restart:

with(Statistics):

f := PDF(Cauchy(0, 1), x)

1/(Pi*(x^2+1))

(1)

m := int(x*f, x=-infinity..+infinity);

undefined

(2)

p := int(x*f, x);

(1/2)*ln(x^2+1)/Pi

(3)

# Naive "proof" : eval(..., infinity) seems to consider infinity as a name (consistent with
# the first line in help(infinity) without any particular property.
# This seems to be confirmed by the value of p1 and p2 : I expected to get infinity instead
# of infinity/Pi.

p1 := eval(p, x=-infinity);
p2 := eval(p, x=+infinity);
p2 - p1;

infinity/Pi

 

infinity/Pi

 

0

(4)

# Correct "proof" :

a := limit(p, x=-infinity);
b := limit(p, x=+infinity);
b-a

infinity

 

infinity

 

undefined

(5)

# Does Maple treat 'infinity' as a number ?

infinity         - infinity;
infinity*2       - infinity*2;
infinity*(1/3)   - infinity*(1/3);
infinity*0.333   - infinity*0.333;
infinity*sqrt(2) - infinity*sqrt(2);
infinity/Pi      - infinity/Pi;

undefined

 

undefined

 

undefined

 

Float(undefined)

 

0

 

0

(6)

limit(sqrt(2)/x, x=0) - limit(sqrt(2)/y, y=0);
limit(Pi/x, x=0)      - limit(Pi/y, y=0);

undefined

 

undefined

(7)

 


 

Download Infinity.mw

Hi,

How can I force the command InsertContent(Worksheet(Group(Input( T )))) to display the variable eq as it appears in label (2) ?

(a screen capture of the output of InsertContent(Worksheet(Group(Input( T )))) is given after the Maple code)

restart:

interface(version)

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

(1)

with(DocumentTools):

with(DocumentTools[Layout]):

eq := piecewise(t < 1, sin(t), cos(t));

C := Cell( Textfield(style=TwoDimOutput,Equation(eq)) ):
T := Table(Column(), widthmode=percentage, width=40, Row(C)):
InsertContent(Worksheet(Group(Input( T )))):

eq := piecewise(t < 1, sin(t), cos(t))

(2)

 



Download Layout.mw

Hi, 

It seems to me that variables (maybe I should have use 'names' instead) become "typed" only once they have been instanciated with ':=' ?

But is it possible in Maple  to do something like that
"I declare that variable V will be of type T even if I do not explicitely instanciate it?"

... or is it here one of the distinction between a "typed CAS" and a "non typed" CAS ?

Thanks in advance

Hi

I would like to use  the Liebniz notation that someone from the technical support posted here
Writing Derivatives at a Point Using Leibniz Notation
to display a formula that is not just a partial derivative but a more complex expression invoking partial derivatives. 
Typically an expression like this one:

2*(Diff(f(mu__1, mu__2), mu__1))^2*lambda__1^2-(Diff(f(mu__1, mu__2), mu__1))^2*mu__1^2+2*(Diff(f(mu__1, mu__2), mu__2))^2*lambda__2^2-(Diff(f(mu__1, mu__2), mu__2))^2*mu__2^2+2*(Diff(f(mu__1, mu__2), mu__1))*(Diff(f(mu__1, mu__2), mu__2))*lambda__1*lambda__2-2*(Diff(f(mu__1, mu__2), mu__1))*mu__1*(Diff(f(mu__1, mu__2), mu__2))*mu__2

Could anyone help me to do this?
Thanks in advance

(PS: I'm still using Maple 2015.2)

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