ComputerUser

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These are questions asked by ComputerUser

http://en.wikipedia.org/wiki/Laguerre_polynomials

http://wenku.baidu.com/view/7d013c8c680203d8ce2f24ee.html  

how to evaluate to equation (5.9) in page 195 from rodrigues formula?

rodrigues := exp(x)*(x^alpha)/n!*Diff(exp(-x)*(x^(n+alpha)), x$n);
rodrigues := subs(x=2*p, rodrigues);
rodrigues := subs(alpha=1/2, rodrigues);

Laguerre
charc := -(-1/(-1+I*X))^alpha/(-1+I*X);
Density := int(-exp(-I*X*u)*(-1/(-1+I*X))^alpha/(-1+I*X), X = -infinity .. infinity);
can not evaluate

Meixner
charc := (1+mean/(-1+exp(I*X)*mean)-mean*exp(I*X)/(-1+exp(I*X)*mean))^gamma;
Density := int(exp(-I*X*u)*(1+mean/(-1+exp(I*X)*mean)-mean*exp(I*X)/(-1+exp(I*X)*mean))^gamma, X = -infinity .. infinity);

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

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);

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