def test_gamma(rnd, a, loc=0, scale=1):
# gamma random variate generator
gamma_dist = RVGs.Gamma(a=a, scale=scale, loc=loc)
# obtain samples
samples = get_samples(gamma_dist, rnd)
# report mean and variance
print_test_results('Gamma',
samples,
expectation=a * scale + loc,
variance=a * scale**2)
def test_fitting_gamma():
print('\nTesting Gamma with a=10, scale=1, loc=2:')
dist = RVGs.Gamma(a=10, scale=1, loc=2)
print(' mean, st dev: ', dist.get_mean_st_dev())
print(' percentile interval: ', dist.get_percentile_interval(alpha=0.05))
data = np.array(get_samples(dist, np.random))
dict_mm_results = RVGs.Gamma.fit_mm(mean=np.average(data),
st_dev=np.std(data),
fixed_location=2)
dict_ml_results = RVGs.Gamma.fit_ml(data=data, fixed_location=2)
print(" Fit:")
print(" MM:", dict_mm_results)
print(" ML:", dict_ml_results)
# plot the fitted distributions
Plot.plot_gamma_fit(data=data,
fit_results=dict_mm_results,
title='Method of Moment')
Plot.plot_gamma_fit(data=data,
fit_results=dict_ml_results,
title='Maximum Likelihood')
import numpy as np
import SimPy.RandomVariateGenerators as RVGs
# a random number generator
rng = np.random.RandomState(seed=0)
# gamma
gamma = RVGs.Gamma(a=0.9835458832943496, loc=0, scale=1.9199027077975956)
# generate 10 realizations from gamma
print('Realizations from gamma:')
for i in range(10):
print(gamma.sample(rng))
# gamma-Poisson
gammaPoisson = RVGs.GammaPoisson(a=0.3693765965041004,
gamma_scale=9.154827879319111,
loc=0)
# generate 10 realizations from gamma-Poisson
print('Realizations from gamma-Poisson:')
for i in range(10):
print(gammaPoisson.sample(rng))
def __init__(self, therapy):
self.therapy = therapy
self.probMatrixRVG = [] # list of dirichlet distributions for transition probabilities
self.lnRelativeRiskRVG = None # normal distribution for the natural log of the treatment relative risk
self.annualStateCostRVG = [] # list of gamma distributions for the annual cost of states
self.annualStateUtilityRVG = [] # list of beta distributions for the annual utility of states
self.annualTreatmentCostRVG = None # gamma distribution for treatment cost
# create Dirichlet distributions for transition probabilities
j = 0
for probs in Data.TRANS_MATRIX:
# note: for a Dirichlet distribution all values of the argument 'a' should be non-zero.
# setting if_ignore_0s to True allows the Dirichlet distribution to take 'a' with zero values.
self.probMatrixRVG.append(RVGs.Dirichlet(
a=probs, if_ignore_0s=True))
j += 1
# treatment relative risk
rr_ci = [0.365, 0.71] # confidence interval of the treatment relative risk
# find the mean and st_dev of the normal distribution assumed for ln(RR)
# sample mean ln(RR)
mean_ln_rr = math.log(Data.TREATMENT_RR)
# sample standard deviation of ln(RR)
std_ln_rr = \
(math.log(rr_ci[1]) - math.log(rr_ci[0])) / (2 * stat.norm.ppf(1 - 0.05 / 2))
# create a normal distribution for ln(RR)
self.lnRelativeRiskRVG = RVGs.Normal(loc=mean_ln_rr,
scale=std_ln_rr)
# create gamma distributions for annual state cost
for cost in Data.ANNUAL_STATE_COST:
# if cost is zero, add a constant 0, otherwise add a gamma distribution
if cost == 0:
self.annualStateCostRVG.append(RVGs.Constant(value=0))
else:
# find shape and scale of the assumed gamma distribution
# no data available to estimate the standard deviation, so we assumed st_dev=cost / 5
fit_output = RVGs.Gamma.fit_mm(mean=cost, st_dev=cost / 5)
# append the distribution
self.annualStateCostRVG.append(
RVGs.Gamma(a=fit_output["a"],
loc=0,
scale=fit_output["scale"]))
# create a gamma distribution for annual treatment cost
if self.therapy == Therapies.MONO:
annual_cost = Data.Zidovudine_COST
else:
annual_cost = Data.Zidovudine_COST + Data.Lamivudine_COST
fit_output = RVGs.Gamma.fit_mm(mean=annual_cost, st_dev=annual_cost / 5)
self.annualTreatmentCostRVG = RVGs.Gamma(a=fit_output["a"],
loc=0,
scale=fit_output["scale"])
# create beta distributions for annual state utility
for utility in Data.ANNUAL_STATE_UTILITY:
# if utility is zero, add a constant 0, otherwise add a beta distribution
if utility == 0:
self.annualStateCostRVG.append(RVGs.Constant(value=0))
else:
# find alpha and beta of the assumed beta distribution
# no data available to estimate the standard deviation, so we assumed st_dev=cost / 4
fit_output = RVGs.Beta.fit_mm(mean=utility, st_dev=utility / 4)
# append the distribution
self.annualStateUtilityRVG.append(
RVGs.Beta(a=fit_output["a"], b=fit_output["b"]))
