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Google 2013 Profit Distribution [Bayesian Inference
Posted on June 5, 2013 @ 10:37:00 AM by Paul Meagher

My last article on the concept of a profit distribution was a bit abstract and lacked a graphic. I wanted to correct this situation by constructing a profit distribution for a company we can all relate to - Google.

In order to make this example realistic, I wanted to know how profitable Google is on a year-to-year basis. To find this info, I consulted Google's investor relations area, specifically their 2013 Financial Tables. Here I learned that the net income for Google in 2011 was approx $9.7 billion, in 2012 it was approx. $10.7 billion. I used these values to come up with some reasonable bounds for their expected profit in 2013 (e.g., between 10 billion and 12.4 billion). I divided up this range in units of .4 billion and estimated the probability that Google's net income (or profit) would fall in each interval. This is what I came up with.

The shape of the profit distribution function reflects my belief that Google will continue to grow and that my best guess is that they will grow by another billion in profit next year. I also believe that there is a greater chance they will earn less than than this amount than that they will earn more than this amount.

Notice that if you sum the percentages (e.g., by converting 45% to .45) that they sum to 1 as all good probability distributions should. My uncertainty regarding the expected profit of Google in 2013 is best captured by a range of probability assignments to profit intervals, than by a single point estimate of how much they might make next year. I don't know that much about Google's business lines and how they will perform this year, but I'm able to use my general knowledge and recently acquired financial statements to come up with a 2013 Profit Distribution for Google. This could be considered my "prior" distribution for Google, one that can be updated according to Bayesian logic as more information comes in.

I used JpGraph library to generate this graph. I modified an example graph from the JpGraph site. FYI, here is the code I used to generate the graph.

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