@marc005 

with(Statistics):p := 0.3;
q := 0.2;
r := 1;
n := 2;
MartinPoisson := (p/((p+2*q*T)/(1+p*T+q*T^2)-(p*T+q*T^2)*(p+2*q*T)/(1+p*T+q*T^2)^2))^r*r^2*T^n/factorial(n);
Dist := subs(T=t,MartinPoisson) assuming t > 0;
MartinDist := Distribution(CDF = unapply(Dist, t)) assuming t > 0; #Change 2
Ran := RandomVariable(MartinDist);
Martindata:= Sample(Ran,10);ex := ExpectedValue(Martindata);  # error
plot(CDF(Ran, x), x = -4 .. 4, legend = "CDF Martin", color = blue); # can plot

finally can draw with above method, is it correct

however

> Martindata := Sample(Ran, 10);Error, (in Statistics:-Sample) FAIL .. FAIL is an invalid range

@marc005 

for A := Array([1,1,1,2,4,4,5.5]):

does it mean that i have to group data into for example 5 groups, where value fall into each group

then first value fall in group 1, second value fall in group 1, 3rd value fall in  group 1

4th value fall in group 2, 5th value fall in group 4, 6th value fall in group 4, 7th fall in group 5

or put raw data in Array A directly?

is it possible to draw this?    

as i would like to investigate this 

p := 0.3;

q := 0.2;

MartinPoisson := (p/((p+2*q*T)/(1+p*T+q*T^2)-(p*T+q*T^2)*(p+2*q*T)/(1+p*T+q*T^2)^2))^r*r^2*T^n/factorial(n);

Dist := subs(T=t,MartinPoisson) assuming t > 0;

MartinDist := Distribution(CDF = unapply(Dist, t)) assuming t > 0; #Change 2

K := unapply(MartinDist(t-1),t);

plot(K, -1 .. 2, thickness = 3);

@marc005 

for A := Array([1,1,1,2,4,4,5.5]):

does it mean that i have to group data into for example 5 groups, where value fall into each group

then first value fall in group 1, second value fall in group 1, 3rd value fall in  group 1

4th value fall in group 2, 5th value fall in group 4, 6th value fall in group 4, 7th fall in group 5

or put raw data in Array A directly?

is it possible to draw this?    

as i would like to investigate this 

p := 0.3;

q := 0.2;

MartinPoisson := (p/((p+2*q*T)/(1+p*T+q*T^2)-(p*T+q*T^2)*(p+2*q*T)/(1+p*T+q*T^2)^2))^r*r^2*T^n/factorial(n);

Dist := subs(T=t,MartinPoisson) assuming t > 0;

MartinDist := Distribution(CDF = unapply(Dist, t)) assuming t > 0; #Change 2

K := unapply(MartinDist(t-1),t);

plot(K, -1 .. 2, thickness = 3);

@Carl Love 

is it possible to add to infinity, without infinity, i can not get generating function

i add first 5 terms and then calculate its characteristic function

i got RootOf(....) in the middle step

@Carl Love 

is it possible to add to infinity, without infinity, i can not get generating function

i add first 5 terms and then calculate its characteristic function

i got RootOf(....) in the middle step

why not ex := ExpectedValue(Empiricaldata) + 1.96 * StandardDeviation(Empiricaldata);

if this method work, why need KS test?

do not know how to use real data into this step instead of Normal

Empiricaldata := Sample(RandomVariable(Normal(2, 1)), 100):

i think that there is a need to draw it first to see the separation

have drawn a graph from counting, the shape is shrinked into straight line, it is not practical way.

any other method. To make a distribution from real data for statistics package?

why not ex := ExpectedValue(Empiricaldata) + 1.96 * StandardDeviation(Empiricaldata);

if this method work, why need KS test?

do not know how to use real data into this step instead of Normal

Empiricaldata := Sample(RandomVariable(Normal(2, 1)), 100):

i think that there is a need to draw it first to see the separation

have drawn a graph from counting, the shape is shrinked into straight line, it is not practical way.

any other method. To make a distribution from real data for statistics package?

@Carl Love 

remove the type nonnegint, 

it got error even if using actual integer instead of infinity in Summation( XXXXX,  n = 0..3);

dimension parameters are required in this form of initializer

is it impossible to do this kind of calculation in maple?

@Carl Love 

remove the type nonnegint, 

it got error even if using actual integer instead of infinity in Summation( XXXXX,  n = 0..3);

dimension parameters are required in this form of initializer

is it impossible to do this kind of calculation in maple?

Summation(DetAn(convert(n,nonnegint))*(z^n)/n!, n=0..infinity) assuming n >= 0;

> `assuming`([Summation(DetAn(k)*z^k/factorial(k), k = 0 .. infinity)], [k >= 0]);
Error, (in assuming) when calling 'DetAn'. Received: 'invalid input: DetAn expects its 1st argument, n, to be of type nonnegint, but received k'
> `assuming`([Summation(DetAn(convert(k, nonnegint))*z^k/factorial(k), k = 0 .. infinity)], [k >= 0]);
Error, (in assuming) when calling '`one of {DetAn, convert, Summation, factorial}`'. Received: 'unrecognized conversion'

got some error when actually use it

Summation(DetAn(convert(n,nonnegint))*(z^n)/n!, n=0..infinity) assuming n >= 0;

> `assuming`([Summation(DetAn(k)*z^k/factorial(k), k = 0 .. infinity)], [k >= 0]);
Error, (in assuming) when calling 'DetAn'. Received: 'invalid input: DetAn expects its 1st argument, n, to be of type nonnegint, but received k'
> `assuming`([Summation(DetAn(convert(k, nonnegint))*z^k/factorial(k), k = 0 .. infinity)], [k >= 0]);
Error, (in assuming) when calling '`one of {DetAn, convert, Summation, factorial}`'. Received: 'unrecognized conversion'

got some error when actually use it

it got error when run in maple 12, after retype -> , then got Error, invalid sequence at 'if' after ->

Error, invalid arrow procedure

DetAn:= (n::nonnegint)-> LinearAlgebra:-Determinant(
Matrix(
n, n,
(i,j)-> if j >= i and (j-i)::even then
(j-i+1)*(j-1)!/(i-1)!*a(j-i+1)*x
elif i-j = 1 then -1
else 0
end if
)
):

it got error when run in maple 12, after retype -> , then got Error, invalid sequence at 'if' after ->

Error, invalid arrow procedure

DetAn:= (n::nonnegint)-> LinearAlgebra:-Determinant(
Matrix(
n, n,
(i,j)-> if j >= i and (j-i)::even then
(j-i+1)*(j-1)!/(i-1)!*a(j-i+1)*x
elif i-j = 1 then -1
else 0
end if
)
):

sys_ode := diff(u,x1(t))=0,diff(u,x2(t))=0,diff(u,x3(t))=0;
dsolve({sys_ode},[x1(t),x2(t),x3(t)]);

it can run but no solution, should it be no solution in method 1 Euler?

succeed to solve separately in method 2, however, dsolve all 3 equations together takes a long time so far still calculating

it seems that it should dsolve separately, however x2(t) can not be dsolved as result is still a differential equation

sys_ode := diff(u,x1(t))=0,diff(u,x2(t))=0,diff(u,x3(t))=0;
dsolve({sys_ode},[x1(t),x2(t),x3(t)]);

it can run but no solution, should it be no solution in method 1 Euler?

succeed to solve separately in method 2, however, dsolve all 3 equations together takes a long time so far still calculating

it seems that it should dsolve separately, however x2(t) can not be dsolved as result is still a differential equation