import numpy as np, pandas as pd, array as a
from scipy.stats import norm
# H0: p1>=p2, HA: p1<p2
# Returns r, which is the proportion of S that should be dedicated to n1 to make the probability of rejecting Ho as large as possible
# given p1, p2, i.e. it returns r which minimizes the variance of the difference
# Assumes that the larger of the two ps is p2 (ie, assumes that p2>p1)
params=pd.read_csv("./scen3_params.csv", sep=",", names=['p1', 'p2', 'S'])
p1=float(params.p1[params.p1.index[0]])
p2=float(params.p2[params.p2.index[0]])
S=int(params.S[params.S.index[0]])
print 'p1', p1, 'p2', p2, 'S', S
c1=p1*(1-p1)
c2=p2*(2-p2)
r=(-2*c1+((2*c1)**2+(4*(c2-c1)*c1))**0.5)/(2*(c2-c1))
r1=(-2*c1-((2*c1)**2+(4*(c2-c1)*c1))**0.5)/(2*(c2-c1))
print r, r1