# How to measure clustering in time duration?

I wish to measure clustering in the duration between stock trading. For example, a trade occurs at 1:59:19 and the next trade follows at 1:59:23 - the inter-trade duration is 4 seconds. I have roughly 50,000 trades per day for a particular stock. I was told that I can square the inter-trade duration in order to capture clustering in trades. Is this correct? What if I have a lot of trades that occur at the same time? Hence, inter-trade duration is 0 seconds. Can this have an impact on my clustering measure?

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But I don't know a reason why you should take the squared delays. Is $s^2$ a sensible score here? To me this sounds like a heuristic.