How to quantify distribution concentration in cdf? For example, let's say I have a list of users, each user has its revenue.
I can plot the cdf of both user and revenue, to see if there is some concentration, for example, may be 40% user contribute 60% revenue, which is not much concentration, like this 

It may also be the case that 1% user contribute to 25% revenue, like this 

My question:


*

*Is there any formal way, best practice, metrics to quantify such concentration (instead of just showing the charts)


This is especially important as sometimes we're very concern about the top revenue users; if it concentrates heavily, then we might need some alert when this happens.
 A: A common way to measure inequality is the Gini coefficient as one of many metrics. 
However, depending on your concern and your business problems, you might want to define a metric on your own. 
For example, if the revenue concentration on too few customers causes problems in the financial balance of the company, one can estimate a turnover probability (per segment or in total) and then perform a Monte Carlo simulation to estimate the probability that the revenue for next month will be decrease by x %. For example, if the CEO states, that the company has to be 90 % sure that the revenue loss (excluding new customers) will be less 10 %, you have the threshold for an alarm.
On the other hand, if revenue of customers is positively correlated with amount of required consulting, hence creating a man power issue, the metric and hence the alarm threshold will be entirely different. If fear of potential fraud is the concern, this will also lead to different numbers.
Or as Douglas W. Hubbard in his book How to measure anything has put it in the chapter Clarifying the measurement problem:

Prior to making a measurement, we need to answer the following:
  
  
*
  
*What is the decision this measurement is supposed to support ?
  
*What is the definition of the thing being measured in terms of observable consequences and how, exactly, does this thing matter to
  the decision being asked ?
  

Based on asking and answering the right questions, your measure of interest can be something as simple as: "If the top 25 % revenue is created by less than 5 customers, raise an alarm".
