Discrete and Continuous Time Statistics I am looking for a precise definition for discrete-time statistics(or tally statistics) and continuous-time statistics (or time-persistent statistic). I found most of the definitions to be qualitative. For example here on page 77 there are two definitions presented. But I personally think the maximum of the number of parts in a queue must be a tally statistics since if we plot it over time, it will be a piecewise constant function. Can anyone suggest a concise and precise definition?
Thanks.

From that book you attached, it is just some very vague discussion. 
I guess discrete-time statistics should be referring to discrete stochastic process, and the other is continuous-time stochastic process.
Check the below link for their definitions. You might need some pre-knowledge about measure theory and probability theory to understand the definition.
https://en.wikipedia.org/wiki/Stochastic_process#Classifications
