|
import numpy as np |
|
import matplotlib.pyplot as plt |
|
|
|
def expected_value(prob_storm, sensitivity, specificity, prob_mold, prob_high_sugar, prob_low_sugar, prob_regular_sugar): |
|
payout_matrix = np.matrix([6000*5+2000*10+2000*15, |
|
5000*5+1000*10+2000*120, |
|
5000*5+1000*10, |
|
4000*5+2500*10+2000*15+1000*30+500*40, |
|
6000*5+2000*10+2000*15, |
|
5000*5+1000*10+2500*15+1500*30]) |
|
payout_matrix = payout_matrix * 12 |
|
|
|
def s_branch(payout_matrix,prob_mold): |
|
return(prob_mold * payout_matrix[0,1] + (1-prob_mold) * payout_matrix[0,2]) |
|
|
|
def ns_branch(payout_matrix,prob_high_sugar,prob_low_sugar,prob_regular_sugar): |
|
return(prob_high_sugar * payout_matrix[0,3] + prob_low_sugar*payout_matrix[0,4] + prob_regular_sugar*payout_matrix[0,5]) |
|
|
|
P_DS = sensitivity * (prob_storm) + (1-sensitivity) * (1-prob_storm) |
|
P_DNS = specificity * (1-prob_storm) + (1-specificity) * prob_storm |
|
P_S_DS = (sensitivity * prob_storm)/P_DS |
|
P_NS_DS = 1 - P_S_DS |
|
|
|
E_val_top = [] |
|
E_val_top.append(payout_matrix[0,0]) |
|
E_val_top.append(s_branch(payout_matrix,prob_mold) * P_S_DS + P_NS_DS * ns_branch(payout_matrix,prob_high_sugar,prob_low_sugar,prob_regular_sugar)) |
|
|
|
P_NS_DNS = (specificity * (1-prob_storm))/P_DNS |
|
P_S_DNS = 1-P_NS_DNS |
|
|
|
E_val_bot = [] |
|
E_val_bot.append(payout_matrix[0,0]) |
|
E_val_bot.append(s_branch(payout_matrix,prob_mold) * P_S_DNS + P_NS_DNS*ns_branch(payout_matrix,prob_high_sugar,prob_low_sugar,prob_regular_sugar)) |
|
|
|
result = np.max(E_val_top) * P_DS + np.max(E_val_bot)* (1-P_DS) |
|
|
|
return (result - payout_matrix[0,0]) |
|
|