validation/src/ValidGamma.mws

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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1692 "restart:\nwith(Sta
tistics):\ngamma_:=RandomVariable(Gamma(1/lambda,k)):\nassume(u>0);\np
df:=subs(u=x-_gamma,PDF(gamma_,u));\ncdf:=subs(u=x-_gamma,CDF(gamma_,u
)):\ncdf2:=simplify(convert(cdf,hypergeom),symbolic);\ncf:=subs(u=x,ex
p(-I*_gamma)*CharacteristicFunction(gamma_,u));\nmu_:=_gamma+Mean(gamm
a_);\nvar_:=Variance(gamma_);\nskew_:=simplify(convert(Skewness(gamma_
),GAMMA),symbolic);\nkurt_:=simplify(convert(Kurtosis(gamma_),GAMMA),s
ymbolic);\nsol:=subs(m='mu',v='var',solve(\{mu_=m,var_=v\},\{k,lambda
\}));\n#qdf:=_gamma+Quantile(gamma_,p);\n#qdf2:=solve(cdf=p,x);\npdfgr
:=map(_u->simplify(convert(_u,hypergeom),symbolic),[diff(pdf, k)/pdf, \+
diff(pdf, lambda)/pdf, diff(pdf, _gamma)/pdf]);\ncdfgr:=map(_u->simpli
fy(convert(_u,hypergeom),symbolic),[diff(cdf, k), diff(cdf, lambda), d
iff(cdf, _gamma)]);\n#dCDFdk:=collect(map(_u->simplify(convert(_u,hype
rgeom),symbolic),convert(diff(subs(_gamma=0,cdf2), k),hypergeometric))
,x);\n#dCDFdlambda:=map(_u->factor(simplify(convert(_u,hypergeom),symb
olic)),diff(cdf2, lambda));\n#dCDFdgamma:=map(_u->simplify(convert(_u,
hypergeom),symbolic),diff(cdf2, _gamma));\ncollect(expand(simplify(fac
tor(convert(subs(_gamma=0,lambda=1,diff(cdf2,k)),'StandardFunctions'))
),trig),k);\nvalnum:=k=1.5,lambda=2.5,_gamma=-0.5;\nevalf(subs(valnum,
x=1,ddf));\nevalf(subs(valnum,x=1,pdf));\nevalf(subs(valnum,x=1,cdf));
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fgr)));\nevalf(subs(valnum,x=1,cdfgr));\nevalf(fsolve(subs(valnum,cdf)
=0.95,x));\nevalf(subs(valnum,mu_));\nevalf(subs(valnum,sqrt(var_)));
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alnum,var_));\nevalf(subs(valnum,[mu_,sqrt(var_)]));\nevalf(subs(sol,m
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