Statistical Distributions and Customer Analytics -3

What have probability distributions to do with predictions about customers? If we are to predict a customer's chances of buying again, or not buying at all, we have to base it on some knowledge about the customer and we need some way to figure out the chances of our guess being right or completely out of reality. Without getting into details of why or how, we will assume that one of leading predictors of repeat purchase is the history of the customer with the company. That history can be quantified in few ways and translated into few variables. When the customer bought, what did they buy and how many times did they buy, what and how. All the combinations of the above variables form an understanding about the customer and can be useful in making some predictions which in turn can feed into prioritizing. One easy and basic form of analysis is RFM, to score the customers and based on those scores, predict their future value. To learn more about RFM, simple online search will result in countless very informative resources. Some very reasonable actions can be taken just by looking at the RFM scores. All customers, contrary to what we like to believe, are not equally important. All customer expectations, beyond a certain level, are not equal either. Understanding those even in simple measures can be very useful to any organization.

In developing understanding about predictions and modelling, the concept of chance of something happening (in our case the customer buying again and quantifying that contribution) given we know something about them (in our case their purchase history) is basically conditional probability, with well some not so basic mathematical derivations. If we know a mathematical function that takes our purchase history variables as input and gives us the probability of that particular customer behavior (purchase) then we have created a model. We have assigned a numerical chance of occurrence to subsets of occurrences which will form the basis of our future predictions. The nature and derivation of that function can vary but whatever function we arrive to will be able to take different values of quantified customer historical behavior and give particular probabilities to each of those. 

For us to figure out if a customer will buy again, and if they do how many or how much they will contribute is a matter of assigning a probability to similar occurrences and then finding the expected purchase value weighted by all the chances or probabilities that we figured out and assigned the mathematical model (or function) to. 

So now we have why we need probability distributions...the two probability distributions that we want to discuss for C1, C2 and C3 still await us...and.we still have work to do to understand how nature of a process ties to probability distributions and functions. Learning is a process in itself....and we can definitely call it continuous....