def logitProbitMixtureFunction(z, N, k, mu, sigma, isLogit):
if isLogit == 1:
density = util.logitDensity(z, mu, sigma)
else:
density = util.probitDensity(z, mu, sigma)
probTerm = util.getBC(N, k) * (z**k) * ((1 - z)**(N - k))
f = probTerm * density
return f
def independentBinomialAnalytic(N, p, c, alpha):
pmfBinomial = np.zeros(N + 1)
for k in range(0, N + 1):
pmfBinomial[k] = util.getBC(N, k) * (p ** k) * ((1 - p) ** (N - k))
cdfBinomial = np.cumsum(pmfBinomial)
varAnalytic = c * np.interp(alpha, cdfBinomial, np.linspace(0, N, N + 1))
esAnalytic = util.analyticExpectedShortfall(N, alpha, pmfBinomial, c)
return pmfBinomial, cdfBinomial, varAnalytic, esAnalytic
def betaBinomialAnalytic(N, c, a, b, alpha):
pmfBeta = np.zeros(N + 1)
den = util.computeBeta(a, b)
for k in range(0, N + 1):
pmfBeta[k] = util.getBC(N, k) * util.computeBeta(a + k,
b + N - k) / den
cdfBeta = np.cumsum(pmfBeta)
varAnalytic = c * np.interp(alpha, cdfBeta, np.linspace(0, N, N + 1))
esAnalytic = util.analyticExpectedShortfall(N, alpha, pmfBeta, c)
return pmfBeta, cdfBeta, varAnalytic, esAnalytic
def getCMF_cr(s, myW, myA, myP, myN, myK):
ps = myP * (1 - myW) + myP * myW * s
f = util.getBC(myN, myK) * np.power(ps, myK) * np.power(1 - ps, myN - myK)
return f * util.gammaDensity(s, myA, myA)
def getProdCMF(g, myRho, myP, myN, myK):
pg = th.computeP(myP, myRho, g)
return np.multiply(util.getBC(myN, myK),
np.power(pg, myK) * np.power(1 - pg, myN - myK))
def getCMF(g, myRho, myP, myN, myK):
pg = th.computeP(myP, myRho, g)
f = util.getBC(myN, myK) * np.power(pg, myK) * np.power(1 - pg, myN - myK)
cmf = f * util.gaussianDensity(g, 0, 1)
return cmf
def bLikelihood(N, k, pDomain):
L = util.getBC(N, k) * (pDomain ** k) * ((1 - pDomain) ** (N - k))
return L / np.abs(np.max(L))