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This is not directly related to doing statistics, but rather presenting statistical data.

I have a set of values $$\{x_i\},{i\in I_t},$$ for each $t\in [0,1]$. Every set of values $\{x_i\}$ for a fixed $t$ gives me a distribution and as $t\to 1$, the distribution of $\{x_i\}$ converges to a particular well-known distribution.

I would like to show this convergence graphically in a similar way how $1/n$ sequence converges to $0$. How can I do that? Are there ways of presenting this data such that it will provide an intuition about how fast the date convergence to that particular distribution?

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