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Suppose we have a 2D distribution of shops in an area. For example, here is a heatmap density plot of (latitude, longitude) location of shops in a province: enter image description here

Now suppose that we "zoom into" the distribution and consider only a tiny window $w:([x_1,x_2],[y_1,y_2])$ inside the whole range of x,y; so that we can have a better insight into how data points (shops) are arranged in the small local neighbourhoods.

The data distribution INSIDE each random window is obviously a subset of the entire data. For example, if we plot shops with latitude between $[42, 42.3]$ and longitude between $[-76, -75.5]$, we get this distribution: (visualized with scatterplot)

enter image description here

In the statistics community, what is the actual name of these "zoomed in" parts of a data distribution?

I want to report that the data distribution is skew in general, but quite uniform in "those small subsets". What are those distributions inside the windows called?

May I say, for example, "micro-distribution" or "partial distribution"?

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    $\begingroup$ Notice that you can always edit a question, not need to delete and ask new question. In fact, we generally discourage deleting and re-asking, in vast majority of cases it will yield a moderator reaction. $\endgroup$ – Tim Jun 3 '20 at 10:17
  • $\begingroup$ @Tim yep, thanks for the hint & sorry for the repost; but I realized that my initial post was so badly written that it drifted all comment to irrelevant subjects (such as the type of the charts, the scale of the features, etc). $\endgroup$ – Ali Jun 3 '20 at 12:01
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    $\begingroup$ Detail view of ... $\endgroup$ – wolfies Jun 3 '20 at 15:10
  • $\begingroup$ If your goal is to talk about some property, you can just say that the property applies "locally" or "in this region" $\endgroup$ – user20160 Jun 3 '20 at 18:15
  • $\begingroup$ @user20160, I am indexing a multidimensional data which splits the data into a grid. I am interested in the data distribution inside each grid cell. Is "local distribution" a common term in statistics? $\endgroup$ – Ali Jun 4 '20 at 16:21
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This would be the conditional distribution, conditional on $x\in[x_1,x_2]$ and $y\in[y_1,y_2]$.

Your phrasing of “zoom in” is descriptive and might be worth including, something like, “We also zoom in on the window to show the conditional distribution...”

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    $\begingroup$ Agree with second paragraph, but I'd be reluctant to use "conditional" for describing data manipulations. Conditional probability is a probabilistic term, here we are talking about filtering the data. I wouldn't mix those. $\endgroup$ – Tim Jun 3 '20 at 11:35

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