Diluted Normalized Earnings Per Share
  
You’re in the ebola abatement business. Each year, the government spends a few bucks on you just to keep you alive as a business, in case, well, you know, a few hundred million people’s faces start melting off.
So your earnings are usually flat. But then, one year, after Miss Malaria’s high school biology class takes a field trip to study monkeys, bats, and beetles in caves in Central Ghana…well, business picks up.
So this year, with the gov having to spend a fortune on ebola abatement, you earn $9.42, and since world awareness has suddenly shot up the most popular Yahoo search term index, next year you still earn $5.17. But then things quiet down, and life goes back to normal, where your earnings are; you could plot some kind of line through them, and if someone asked you what normal earnings are in your little ebola abatement company. you could say that your normalized earnings are about $1.20.
Fortunately, making out with a Nigerian fruit bat is not normal, so...you probably don’t have to worry about contracting ebola.
Anyway, you have diluted normalized earnings—how are they diluted? The company could have a sudden bump in earnings from something like the gov spending a ton this week. It could also have earnings diluted from a need to spend more on marketing or key employees, or settling a sexual harassment suit brought by caged monkeys, etc. Yeah, you don't want one of these. It's hard enough to just make your earnings number without all the hassle from dilutive forces always at work against you.