def independentPoissonAnalytic(N, c, myLam, alpha):
pmfPoisson = np.zeros(N + 1)
for k in range(0, N + 1):
pmfPoisson[k] = util.poissonDensity(myLam, k)
cdfPoisson = np.cumsum(pmfPoisson)
varAnalytic = c * np.interp(alpha, cdfPoisson, np.linspace(0, N, N + 1))
esAnalytic = util.analyticExpectedShortfall(N, alpha, pmfPoisson, c)
return pmfPoisson, cdfPoisson, varAnalytic, esAnalytic
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 logitProbitBinomialAnalytic(N, c, mu, sigma, alpha, isLogit):
pmf = np.zeros(N + 1)
for k in range(0, N + 1):
pmf[k], err = nInt.quad(logitProbitMixtureFunction,
0,
1,
args=(N, k, mu, sigma, isLogit))
cdf = np.cumsum(pmf)
varAnalytic = c * np.interp(alpha, cdf, np.linspace(0, N, N + 1))
esAnalytic = util.analyticExpectedShortfall(N, alpha, pmf, c)
return pmf, cdf, varAnalytic, esAnalytic
def poissonMixtureAnalytic(N, myC, a, b, alpha, whichModel):
pmfMixture = np.zeros(N + 1)
for k in range(0, N + 1):
pmfMixture[k], err = nInt.quad(poissonMixtureIntegral,
0,
k + 1,
args=(k, a, b, N, whichModel))
cdfMixture = np.cumsum(pmfMixture)
varAnalytic = myC * np.interp(alpha, cdfMixture, np.linspace(0, N, N + 1))
esAnalytic = util.analyticExpectedShortfall(N, alpha, pmfMixture, myC)
return pmfMixture, cdfMixture, varAnalytic, esAnalytic
def poissonGammaAnalytic(N, c, a, b, alpha):
pmfPoisson = np.zeros(N + 1)
q = np.divide(b, b + 1)
den = math.gamma(a)
for k in range(0, N + 1):
num = np.divide(math.gamma(a + k), scipy.misc.factorial(k))
pmfPoisson[k] = np.divide(num, den) * np.power(q, a) * np.power(
1 - q, k)
cdfPoisson = np.cumsum(pmfPoisson)
varAnalytic = c * np.interp(alpha, cdfPoisson, np.linspace(0, N, N + 1))
esAnalytic = util.analyticExpectedShortfall(N, alpha, pmfPoisson, c)
return pmfPoisson, cdfPoisson, varAnalytic, esAnalytic