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When we use prediction, we can only say levels.

For example: We have 500 sample data for our walking range. And let's say 90 percentile is 16.0 km and 10th percentile is 0.78 km. Well, can only say that there's a 80% probability that we will walk between 0.78 km - 16 km. Or 90% we will walk less than 26 km and 90% we will walk more than 0.78 km. But is there a way to say 75% we will walk that much instead of giving a range?

Or is percentile the only well-known way to use for such predictions? I know we can use regressions, providing more information but the only information we have is this.

EDIT: We can only say today we have walked 9km which is 75th percentile. But how can we say that there's a 75% probability to walk 9km tomorrow? Or simply can't we?

EDIT 2: To be more clear. Is there a way to say: Tomorrow 75% you will walk 8km instead of 75% you will walk less than 8km?

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closed as unclear what you're asking by user158565, jbowman, BruceET, mkt - Reinstate Monica, Peter Flom - Reinstate Monica Jun 25 at 11:03

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You are essentially looking for a , specifically for a $[0,0.75]$ interval. Equivalently, you could read up on quantile forecasts for a 75% quantile.

There are many ways to calculate such a quantile prediction, including:

  • parametric approaches, as in ARIMA: you assume normal noise in the data generating process, predict both the mean and the variance and extract the percentile from the predictive density
  • resampling-based approaches, as in most Bayesian treatments: you derive a predictive density and sample from that
  • "direct" approaches, where you directly predict your quantile as a point forecast (e.g., Gneiting, 2011)

Whether either one of these is successful will depend on your training data and on the percentiles you are aiming at. Very high (or low) percentiles are typically harder.

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  • $\begingroup$ Thank you for your answer. The problem is, can you say that 75% you will walk 8km tomorrow. Can can we still say that 75% you will walk less than 8km? I mean this is the confusing part here. We can only say this: After walk, you look at the length of walk and you can say that it's #th percentile. But we can say this after job completed. $\endgroup$ – Don Coder Jun 25 at 18:19
  • $\begingroup$ Ah. I may have misunderstood. If you want to have a probability of walking exactly 75km, then you need a discrete predictive probability distribution (continuous distributions have zero probability for each single event). In that case, you can simply report the predicted probability for 75km. (I don't think a discrete probability makes a lot of sense for distances walked, since distances are inherently continuous.) $\endgroup$ – S. Kolassa - Reinstate Monica Jun 25 at 18:54
  • $\begingroup$ Stephan, i do quantile forecasts but it gives me a wide range. For example i can only say there's 75% probability that i will walk less than 7km and more then 1km. But I can not say 75% probability, i will walk 5km tomorrow. So I'm trying to figure out if this is possible? Instead of getting a range, is it possible to give exact km and say 75% i will walk that much. Sorry for my English :( $\endgroup$ – Don Coder Jun 25 at 19:21
  • $\begingroup$ It will not be possible with a continuous predictive distribution, but it will be with a discrete one. Look into count data models. (I don't think they are appropriate here, and I don't really see why you would be interested in a probability for an exact distance.) $\endgroup$ – S. Kolassa - Reinstate Monica Jun 26 at 5:54
  • $\begingroup$ I am trying to complete a study for my school i am working on. So we are trying to predict students daily walking distances. There's this idea comes from $\endgroup$ – Don Coder Jun 26 at 10:39

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