def poissonMixtureIntegral(s, k, a, b, N, whichModel):
pDensity = util.poissonDensity(N * s, k)
if whichModel == 0:
mixDensity = util.logNormalDensity(s, a, b)
elif whichModel == 1:
mixDensity = util.weibullDensity(s, a, b)
f = pDensity * mixDensity
return f
def poissonMixtureMoment(s, a, b, momentNumber, whichModel):
v0 = 1 - np.exp(-s)
if whichModel == 0:
myDensity = util.logNormalDensity(s, a, b)
else:
myDensity = util.weibullDensity(s, a, b)
f = np.power(v0, momentNumber) * myDensity
return f
def poissonTransformedMixtureMoment(s, a, b, momentNumber, whichModel):
vy = -np.log(1 - s)
jacobian = np.divide(1, 1 - s)
if whichModel == 0:
psDensity = util.logNormalDensity(vy, a, b) * jacobian
elif whichModel == 1:
psDensity = util.weibullDensity(vy, a, b) * jacobian
myMoment = (s**momentNumber) * psDensity
return myMoment
def getYDensity(y, p1, p2, whichModel, v=0):
if whichModel == 0:
return util.gaussianDensity(y, 0, 1)
elif whichModel == 1:
return util.betaDensity(y, p1, p2)
elif whichModel == 2:
return util.gammaDensity(y, p2, p2)
elif whichModel == 3:
return util.gaussianDensity(y, 0, 1)
elif whichModel == 4:
return util.gaussianDensity(y, 0, 1)
elif whichModel == 5:
return util.weibullDensity(y, p1, p2)
elif whichModel == 6:
return util.gaussianDensity(y, 0, 1) * util.chi2Density(v, p2)