On the percentile of a product of normal distributions, I wrote this Python script which shows that the 5th percentile of a product of normally distributed random variables will in general be a product of much higher percentiles (in this case, the 16th percentile):
import random
MU = 100 SIGMA = 10 N_SAMPLES = 10 ** 6 TARGET_QUANTILE = 0.05 INDIVIDUAL_QUANTILE = 83.55146375 # From Google Sheets NORMINV(0.05,100,10)
samples.sort() # The sampled 5th percentile product product_quantile = samples[int(N_SAMPLES * TARGET_QUANTILE)] implied_individual_quantile = product_quantile ** (1/3) implied_individual_quantile # ~90, which is the *16th* percentile by the empirical rule
I apologize for overstating the degree to which this reversion occurs in my original reply (which claimed an individual percentile of 20+ to get a product percentile of 5), but I hope this Python snippet shows that my point stands.
I did explicitly say that my calculation wasn’t correct. And with the information on hand I can’t see how I could’ve done better.
This is completely fair, and I’m sorry if my previous reply seemed accusatory or like it was piling on. If I were you, I’d probably caveat your analysis’s conclusion to something more like “Under RP’s 5th percentile weights, the cost-effectiveness of cage-free campaigns would probably be lower than that of the best global health interventions”.
Thanks for being charitable :)
On the percentile of a product of normal distributions, I wrote this Python script which shows that the 5th percentile of a product of normally distributed random variables will in general be a product of much higher percentiles (in this case, the 16th percentile):
I apologize for overstating the degree to which this reversion occurs in my original reply (which claimed an individual percentile of 20+ to get a product percentile of 5), but I hope this Python snippet shows that my point stands.
This is completely fair, and I’m sorry if my previous reply seemed accusatory or like it was piling on. If I were you, I’d probably caveat your analysis’s conclusion to something more like “Under RP’s 5th percentile weights, the cost-effectiveness of cage-free campaigns would probably be lower than that of the best global health interventions”.