def qq_comp_binom_poiss_comp_determn_poiss(l,p,poisson_mu=4.0,n_sim=1000,\
alpha_hats = np.arange(0.0001,1.0,1e-3)):
alphas = np.zeros(len(alpha_hats))
isfs = int(l * p) * poisson.isf(alpha_hats, poisson_mu)
for _ in range(n_sim):
comp_binom_rv = CompoundPoisson.rvs_s(poisson_mu,
l,
p,
compound='binom')
alphas += (comp_binom_rv > isfs) / n_sim
return alphas, alpha_hats
def plot_alpha_beta(n=32,p=.3):
dist_rvs_compound = lambda lmb,t: CompoundPoisson.rvs_s(lmb*t,n,p,compound='log')
dist_rvs_poisson = lambda lmb,t: poisson.rvs(lmb*t)
alphas1,betas1,alpha_hats1 = run_simulns(fn=dist_rvs_poisson)
alphas2,betas2,alpha_hats2 = run_simulns(fn=dist_rvs_compound, n_sim=50000)
plt.plot(alpha_hats1,alphas1,label='UMP poisson on poisson')
plt.plot(alpha_hats2,alphas2,label='UMP poisson on compound poisson')
plt.xlabel('Alpha')
plt.ylabel('Beta')
plt.legend(facecolor="black", edgecolor="black")
fig.savefig("C:\\Users\\ropandey\\OneDrive\\MSFTProj\\HypothTestAIR\\alpha_hat_w_alpha.png", \
facecolor=fig.get_facecolor(), transparent=True)
plt.close()
def binom_comp_poisson_alpha_beta():
dist_rvs_poisson = lambda lmb,t: poisson.rvs(lmb*t)
alphas1,betas1,alpha_hats1 = run_simulns(fn=dist_rvs_poisson)
print("Poisson done!")
dist_rvs_compound = lambda lmb,t: CompoundPoisson.rvs_s(lmb*t,2,.4,compound='binom')
alphas2,betas2,alpha_hats2 = run_simulns(fn=dist_rvs_compound, n_sim=50000)
print("l=2 done")
dist_rvs_compound = lambda lmb,t: CompoundPoisson.rvs_s(lmb*t,3,.4,compound='binom')
alphas3,betas3,alpha_hats3 = run_simulns(fn=dist_rvs_compound, n_sim=5000)
print("l=3 done")
dist_rvs_compound = lambda lmb,t: CompoundPoisson.rvs_s(lmb*t,4,.4,compound='binom')
alphas4,betas4,alpha_hats4 = run_simulns(fn=dist_rvs_compound, n_sim=5000)
print("l=4 done")
dist_rvs_compound = lambda lmb,t: CompoundPoisson.rvs_s(lmb*t,5,.4,compound='binom')
alphas5,betas5,alpha_hats5 = run_simulns(fn=dist_rvs_compound, n_sim=5000)
print("l=5 done")
dist_rvs_compound = lambda lmb,t: CompoundPoisson.rvs_s(lmb*t,6,.4,compound='binom')
alphas6,betas6,alpha_hats6 = run_simulns(fn=dist_rvs_compound, n_sim=5000)
print("l=5 done")
dist_rvs_compound = lambda lmb,t: CompoundPoisson.rvs_s(lmb*t,10,.4,compound='binom')
alphas10,betas10,alpha_hats10 = run_simulns(fn=dist_rvs_compound, n_sim=5000)
print("l=10 done")
dist_rvs_compound = lambda lmb,t: CompoundPoisson.rvs_s(lmb*t,20,.4,compound='binom')
alphas20,betas20,alpha_hats20 = run_simulns(fn=dist_rvs_compound, n_sim=5000)
print("all done")
color_list = sns.color_palette("RdBu_r", 20)
color_list = color_list.as_hex()
plt.plot(alphas1,betas1,label='UMP poisson on poisson',color='black')
plt.plot(alphas2,betas2,label='UMP poisson on compound poisson l=2',color=color_list[1])
plt.plot(alphas3,betas3,label='UMP poisson on compound poisson l=3',color=color_list[2])
plt.plot(alphas4,betas4,label='UMP poisson on compound poisson l=4',color=color_list[3])
plt.plot(alphas5,betas5,label='UMP poisson on compound poisson l=5',color=color_list[4])
plt.plot(alphas6,betas6,label='UMP poisson on compound poisson l=6',color=color_list[5])
plt.plot(alphas10,betas10,label='UMP poisson on compound poisson l=10',color=color_list[9])
plt.plot(alphas20,betas20,label='UMP poisson on compound poisson l=20',color=color_list[19])
plt.xlabel('Alpha')
plt.ylabel('Beta')
plt.legend()
plt.show()
plt.plot(alpha_hats1,alphas1,label='UMP poisson on poisson')
plt.plot(alpha_hats2,alphas2,label='UMP poisson on compound poisson l=2',color=color_list[1])
plt.plot(alpha_hats3,alphas3,label='UMP poisson on compound poisson l=3',color=color_list[2])
plt.plot(alpha_hats4,alphas4,label='UMP poisson on compound poisson l=4',color=color_list[3])
plt.plot(alpha_hats5,alphas5,label='UMP poisson on compound poisson l=5',color=color_list[4])
plt.plot(alpha_hats6,alphas6,label='UMP poisson on compound poisson l=6',color=color_list[5])
plt.plot(alpha_hats10,alphas10,label='UMP poisson on compound poisson l=10',color=color_list[9])
plt.plot(alpha_hats20,alphas20,label='UMP poisson on compound poisson l=20',color=color_list[19])
plt.xlabel('Type-1 error')
plt.ylabel('False positive rate')
plt.legend()
plt.show()
def tst_ump_poisson_on_comp_poisson():
## Only works for l=1!
l = 1
p = .3
beta_1 = UMPPoisson.beta_on_poisson_closed_form(t1=25,t2=25,\
lmb_base=12*l*p,effect=1*l*p,alpha=0.1)
dist_rvs_compound = lambda lmb, t: CompoundPoisson.rvs_s(
lmb * t, l, p, compound='binom')
alphas, betas, alpha_hats = alpha_beta_curve(dist_rvs_compound,n_sim=10000, lmb=12, t1=25, t2=25, \
scale=1.0, dellmb = 1)
ix = np.argmin((alpha_hats - 0.1)**2)
print(alpha_hats[ix])
beta_2 = betas[ix]
assert (beta_2 - beta_1) / beta_1 < 1e-3
def tst_ump_poisson_on_determinist_cmpnd_alpha(plot=False):
alphas,alpha_hats,pois_mas = xtst.UMPPoisson.alpha_on_determinist_compound_closed_form(\
lmb=10.0,t1=10,t2=10,l=3)
ix = np.argmin((alpha_hats - 0.05)**2)
print(alpha_hats[ix])
alpha = alphas[ix]
l = 3
p = 1.0
dist_rvs_compound = lambda lmb, t: CompoundPoisson.rvs_s(
lmb * t, l, p, compound='binom')
alphas1, betas1, alpha_hats1 = alpha_beta_curve(dist_rvs_compound,n_sim=10000, \
lmb=10, t1=10, t2=10, scale=1.0, dellmb = 0)
ix = np.argmin((alpha_hats1 - 0.05)**2)
print(alpha_hats1[ix])
alpha1 = alphas1[ix]
if plot:
plt.plot(alpha_hats, alphas, label='Closed form')
plt.plot(alpha_hats1, alphas1, label='Simulated')
plt.legend()
plt.show()
assert abs(alpha1 - alpha) / alpha1 < 1e-3
def alpha_plots(n=32,p=.3):
dist_rvs_compound = lambda lmb,t: CompoundPoisson.rvs_s(lmb*t,n,p,compound='log')
dist_rvs_poisson = lambda lmb,t: poisson.rvs(lmb*t)
alphas1,betas1,alpha_hats1 = run_simulns(fn=dist_rvs_compound, n_sim=5000, t1=10.0,t2=3.0)
alphas2,betas2,alpha_hats2 = run_simulns(fn=dist_rvs_compound, n_sim=5000, t1=3.0,t2=10.0)
alphas3,betas3,alpha_hats3 = run_simulns(fn=dist_rvs_compound, n_sim=5000, t1=10.0,t2=10.0)
alphas4,betas4,alpha_hats4 = run_simulns(fn=dist_rvs_compound, n_sim=5000, t1=3.0,t2=3.0)
alphas5,betas5,alpha_hats5 = run_simulns(fn=dist_rvs_compound, n_sim=5000, lmb=5.0, t1=10.0,t2=10.0)
plt.plot(alpha_hats1,alphas1,label="t1=10; t2=3; lmb=20")
plt.plot(alpha_hats2,alphas2,label="t1=3; t2=10; lmb=20")s
plt.plot(alpha_hats3,alphas3,label="t1=10; t2=10; lmb=20")
plt.plot(alpha_hats4,alphas4,label="t1=3; t2=3; lmb=20")
plt.plot(alpha_hats5,alphas5,label="t1=10; t2=10; lmb=5")
plt.xlabel('Alpha you set')
plt.ylabel('Alpha you get')
plt.legend(facecolor="black", edgecolor="black")
fig.savefig("C:\\Users\\rohit\\OneDrive\\MSFTProj\\HypothTestAIR\\alpha_mapping_no_change.png", \
facecolor=fig.get_facecolor(), transparent=True)
plt.close()
from stochproc.hypothesis.hypoth_tst_simulator import run_simulns
from stochproc.count_distributions.compound_poisson import CompoundPoisson
# mpl.rcParams.update({'text.color' : "white",
# 'axes.labelcolor' : "white",
# 'xtick.color' : "white",
# 'ytick.color' : "white",
# "axes.edgecolor" : "white"})
# fig, ax = plt.subplots(facecolor='black')
# #ax.set_axis_bgcolor("black")
# ax.set_facecolor("black")
#fig, ax = plt.subplots()
dist_rvs_compound = lambda lmb,t: CompoundPoisson.rvs_s(lmb*t,32,.3,compound='binom')
dist_rvs_poisson = lambda lmb,t: poisson.rvs(lmb*t)
def plot_tests_on_distributions():
alphas1,betas1,alpha_hats1 = run_simulns(fn=dist_rvs_poisson)
alphas2,betas2,alpha_hats2 = run_simulns(fn=dist_rvs_compound, n_sim=50000)
alphas3,betas3,alpha_hats3 = run_simulns(fn=dist_rvs_interarrivalw, n_sim=5000)
alphas4,betas4,alpha_hats4 = run_simulns(fn=dist_rvs_interarrivalw, n_sim=5000, scale=25.0)
alphas5,betas5,alpha_hats5 = run_simulns(fn=dist_rvs_interarrivalw, n_sim=5000, scale=1/10.0)
plt.plot(alphas1,betas1,label='UMP poisson on poisson')
plt.plot(alphas2,betas2,label='UMP poisson on compound poisson')
plt.plot(alphas3,betas3,label='UMP poisson on interarrival weibull')
plt.plot(alphas4,betas4,label='UMP poisson sc:25.0 on interarrival weibull')
plt.plot(alphas5,betas5,label='UMP poisson sc:0.1 on interarrival weibull')
plt.xlabel('Alpha')
def rvs_comp_poisson(t, theta=5, m=100):
p = t / (theta + t)
lamb = -m * np.log(1 - p)
log_rvs = lambda: logser.rvs(p)
return CompoundPoisson.rvs_s_1(log_rvs, lamb)