# Quantifying an increasing spacing between data points

Is there a measure or statistic that could quantify a steady increase in the spacing between data points in a time series?

For instance, in the figure, the points are clustered and dense near 0, but then they become more and more sparse.

Thanks

• by "variance" I think you mean "spacing", so the time dependence of the mean spacing should give you the information you want. – Carlo Beenakker Jan 28 '18 at 13:02
• Hi Carlo, thank you for the precision. That's what I meant! Is there any reference or formulation that you know of? – Raskol Jan 28 '18 at 13:21

Yes, there is the inhomogeneous Poisson process with rate $\lambda(t)$.