ComputerUser

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These are questions asked by ComputerUser

Custom distribution
restart;
with(Statistics):
Density := 2*exp(-t^2)*sqrt(Pi);
Dist := int(Density, t);

a.

RealDist := Distribution(Dist(t-1));
Error, (in Statistics:-Distribution) unexpected argument(s): Pi(t)*(erf(t))(t)

b.

RealDist := Distribution(PDF = (t->2*exp(-t^2)*sqrt(Pi)), CDF = (t->Dist(t)), Mean = 1);

RealDist := Distribution(PDF = (t->2*exp(-t^2)*sqrt(Pi)), CDF = (t->Dist(t)));
X:=RandomVariable(RealDist(t-1));

a.
charc := 1/exp(-(1/4)*i^2*X^2);
Density := int(exp(-I*X*u)*charc, X = -infinity .. infinity);

b.
charc := 1/(i*X/(exp(i*X)-1))^n;
Density := int(exp(-I*X*u)*charc, X = -infinity .. infinity);

c.
Density := int(exp(-I*X*u)/(((-1+exp(i*X)+p)/(p*exp(i*X)))^y*(1/exp(i*X))^n), X = -infinity .. infinity);

d.
Density := int(exp(-I*X*u)/(ln(exp(i*X))/(exp(i*X)-1))^n, X = -infinity .. infinity);

e.
charc := 1+i*X/(i*X-1);
Density := int(exp(-I*X*u...

i use previous post link to derive again for weibull, the final integration seems can not be integrated,

any things need to notice?

Weibull
WeibullDist := (η/rho)*((x/rho)^(η-1))*exp(-((x/rho)^η));
WeibullDist := 1-summation((η/rho)*((x/rho)^(η-1))*exp(-((x/rho)^η)),x=0..k-1);
WeibullDist := int((η*z)*(((k-1)*z)^(η-1))*exp(-(((k-1)*z)^η)),z=0..1/rho);
WeibullDist := int((η*z)*(((k-1)*z)^(η-1))*exp(-(((k-1)*z)^η)),z=0..1/rho);

expand(convert(simplify(GammaDensity, size),exp)),size)

www.stat.rice.edu/~dobelman/textfiles/DistributionsHandbook.pdf

i use the derivation of gamma in above book to derive density again, but fail

GammaDist := int((lambda^k)*(z^(k-1))*(exp(-lambda*z))/(k-1)!, z=0..t);
GammaDensity := diff(GammaDist, t);

GammaDensity := (b^a)*(x^(a-1))*exp(-x*b)/GAMMA(a);

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