# How to merge probability distributions / histograms?

I'm wondering how to create a better predictive distribution based on past conditional events in a stock.

For example, suppose I observe that historically after a 5% drop in a stock, tomorrow's distribution has a mean of 1% and a variance of 2%

Let's call it conditional distribution 1 N [1%,2%]

But then supposed I observe also that historically, since tomorrow is Friday, that every Friday the stock has a mean of 0% and a variance of 3%

Let's call it conditional distribution 2 N [0%,3%]

Both of these distributions give different results for tomorrow and my intuition tells me that I should take both pieces of data into account to create a new conditional distribution for tomorrow (Friday).

How would I approach and create one distribution for what's going to happen tomorrow?

I don't think averaging out the mean and variance is the correct approach to this? Would I add weights to the data and create a new distribution by merging the data from both distributions? Would I somehow integrate the normal distributions?

Would appreciate any help.

• I think what you are really after here is determining how to obtain a more predictive model. This can really only be done by evaluating possible models against historical data that was not used to build your model. I'd recommend you take all your candidate prediction models and evaluate each of their historical performances and then make a prediction for tomorrow's stock price using the best performing model historically. That model might include the model with day of week or might not. Aug 17, 2020 at 0:44
• So, one thing that may also be confusing you, me, and others, is that you wrote "But then suppose I observe also..." which implies that you have observed tomorrow is Friday AND you have observed a 5% drop. In this case, your second distribution already contains both the information from distribution 1 (that distribution examines the mean and variance historically of all stocks price on Fridays following a 5% drop). Aug 17, 2020 at 0:59