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I have a dataset of revenue per customer per month. I want to have a measure of the diversity of this revenue, for which (to me) there are two aspects:

  • More customers is better
  • A more equal distribution of revenue per customer is better

So, for example, if I have three customers each generating 50 per month in month 1, then if I have three customers generating 50 and one generating 5 in month 2, then I've had an improvement (more customers). Likewise, in month 3, I have two generating 50, one generating 45 and one generating 10, then I've had an improvement (more equal distribution).

I have tried calculating a Gini coefficient per month. And whilst this captures the equal distribution-of-revenue element, it doesn't capture the more-customers-is-better element.

I'm thinking that as there are two aspects of value I need to somehow capture a weighting between them?

I'm not a statistician, so I would be grateful if you could add a layman's answer as well as any technical response.

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  • $\begingroup$ Perhaps your example for Month 1 is poorly chosen, because its values have null standard deviation. If your purpose is to convincingly bound the result away from 0, then a 95% left-sided t confidence limit might work: $\bar X - t^*S/\sqrt{n},$ where $t^*$ cuts 5% from the upper tail of Student's t dist'n with $n-1$ degrees of freedom. $\endgroup$ – BruceET Dec 19 '18 at 17:43

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