i get it. Thank you.

it would take many steps. Anyway, i can do it

i get it. Thank you.

it would take many steps. Anyway, i can do it

even if changed to Variance(X) = StandardDeviation(A)^2

the graph of beta is still a vertical straight and far apart from distribution of real data,

why?

even if changed to Variance(X) = StandardDeviation(A)^2

the graph of beta is still a vertical straight and far apart from distribution of real data,

why?

a can be any function

or 

you can try a := t -> t^2;

a can be any function

or 

you can try a := t -> t^2;

@marc005 

i discover sample size = 10, it return the same result

if size = 20 always return reject

and size = 10 always return accept

what do it mean ? 

does it mean that i should not buy or sell this time?

@marc005 

i discover sample size = 10, it return the same result

if size = 20 always return reject

and size = 10 always return accept

what do it mean ? 

does it mean that i should not buy or sell this time?

@marc005 

i discover it sometimes return reject, or sometimes return accept

does it suggest that not to do anything if reject now? or only reflect past situation?

if only reflect past situation, any books or paper written a hypothesis testing can reflect in coming future?

@marc005 

i discover it sometimes return reject, or sometimes return accept

does it suggest that not to do anything if reject now? or only reflect past situation?

if only reflect past situation, any books or paper written a hypothesis testing can reflect in coming future?

@marc005 

moreover, what is signaficant testing for ? when i get false from this testing for real equity data, what do it reject?

if it mean that there is significant difference between the data sets,

what do "significant difference between the data sets" mean?

anything that failed to do when there is significant difference between the data sets?

@marc005 

moreover, what is signaficant testing for ? when i get false from this testing for real equity data, what do it reject?

if it mean that there is significant difference between the data sets,

what do "significant difference between the data sets" mean?

anything that failed to do when there is significant difference between the data sets?

@marc005 

my goal is to replace exp(-r*x) with FF2 where 0<=p<=1 and 0 <= q <=1

when you plot FF2, you will see it is like exp(-x) between 0 and 1, when n is larger, converge faster

through the method of making Poisson, and Gamma Function

derive VG of Madan again

but i failed at step

tm := simplify(int(expand(1/(rho*sqrt(2*Pi*g))*exp(-((X-theta*g)^2)/(2*g*rho^2))*MartinDensity),g=0..infinity));

Could you make this derive steps success?

P := p*z+q*z^2;
FF2 := P/(1+P);
FF2 := subs(z=T, (1/(diff(FF2, z)/(subs(z=0,diff(FF2, z)))))^r); # this step invent by me to micmic exp(x)

After find P(n=1 | r,M), P(n=2 | r,M), P(n=3 | r,M)

with(Statistics):
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(piecewise(t>1,Dist,0),t));
MartinDist := Distribution(CDF = unapply(Dist, t)) assuming t > 0; #Change 2
X:=RandomVariable(MartinDist);
MartinDensity := PDF(X,t);
MartinDensity := subs(t=x, MartinDensity);
MartinDensity := subs(n=a, MartinDensity);
MartinDensity := subs(r=b, MartinDensity);
MartinDensity := subs(a=t/v, MartinDensity);
MartinDensity := subs(x=g, MartinDensity);
MartinDensity := subs(b=1/v, MartinDensity);
MartinDensity := simplify(MartinDensity);
tm := simplify(int(expand(1/(rho*sqrt(2*Pi*g))*exp(-((X-theta*g)^2)/(2*g*rho^2))*MartinDensity),g=0..infinity));
a := int(exp(i*X*u)*tm, X = -infinity .. infinity);
Martin := simplify(a, power) assuming rho > 0, theta > 0, v > 0;
MartinMadan := subs(i^2=-1,subs(u=-i,Martin));

@marc005 

my goal is to replace exp(-r*x) with FF2 where 0<=p<=1 and 0 <= q <=1

when you plot FF2, you will see it is like exp(-x) between 0 and 1, when n is larger, converge faster

through the method of making Poisson, and Gamma Function

derive VG of Madan again

but i failed at step

tm := simplify(int(expand(1/(rho*sqrt(2*Pi*g))*exp(-((X-theta*g)^2)/(2*g*rho^2))*MartinDensity),g=0..infinity));

Could you make this derive steps success?

P := p*z+q*z^2;
FF2 := P/(1+P);
FF2 := subs(z=T, (1/(diff(FF2, z)/(subs(z=0,diff(FF2, z)))))^r); # this step invent by me to micmic exp(x)

After find P(n=1 | r,M), P(n=2 | r,M), P(n=3 | r,M)

with(Statistics):
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(piecewise(t>1,Dist,0),t));
MartinDist := Distribution(CDF = unapply(Dist, t)) assuming t > 0; #Change 2
X:=RandomVariable(MartinDist);
MartinDensity := PDF(X,t);
MartinDensity := subs(t=x, MartinDensity);
MartinDensity := subs(n=a, MartinDensity);
MartinDensity := subs(r=b, MartinDensity);
MartinDensity := subs(a=t/v, MartinDensity);
MartinDensity := subs(x=g, MartinDensity);
MartinDensity := subs(b=1/v, MartinDensity);
MartinDensity := simplify(MartinDensity);
tm := simplify(int(expand(1/(rho*sqrt(2*Pi*g))*exp(-((X-theta*g)^2)/(2*g*rho^2))*MartinDensity),g=0..infinity));
a := int(exp(i*X*u)*tm, X = -infinity .. infinity);
Martin := simplify(a, power) assuming rho > 0, theta > 0, v > 0;
MartinMadan := subs(i^2=-1,subs(u=-i,Martin));

@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