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I'm reading an older statistical paper (1994 - not too old, but before computers were in every office) and the author writes the following:

From (#) we see that $\mathbf P$ satisfies the distributional equation $$\mathbf P \stackrel{st}{=}\theta_1\mathbf D + (1 - \theta_1)\mathbf P$$

I should add for clarity that $\mathbf P$ is a vector obtained by applying a random probability measure on a measurable partition of the sample space and $\mathbf D$ is a series of indicator variables with respect to the same partition.

I think I understand what's going on in the paper, and it would make sense based on this (and other uses in the paper) for this symbol to indicate equality in distribution - but I've never seen that notation before. (I've always seen it written with a lower case $d$: (e.g. $\stackrel{d}{=}$). Is the "obvious" definition correct, or am I missing something subtle?

For anyone interested (or who found my explanation overly simplistic), a link to the whole paper is here: http://www3.stat.sinica.edu.tw/statistica/j4n2/j4n216/j4n216.htm It should be open access. My goal is simply to verify the meaning of the symbol.

Thanks!

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  • $\begingroup$ No clue... see Symbols based on equality. $\endgroup$ – Mauro ALLEGRANZA Apr 20 '18 at 7:02
  • $\begingroup$ Yeah... I tried google multiple times before posting here. I found a lot of sites like that, but this symbol has proven elusive - I have yet to find it anywhere other than this paper - let alone a possible meaning for it. $\endgroup$ – Melissa Key Apr 20 '18 at 7:15
  • $\begingroup$ I apologize, to me, the "obvious" definition isn't going to be standard equality for the very reason you mention. My best guess is equality in distribution, I just don't know how you get "equality in distribution" from an "st". $\endgroup$ – Melissa Key Apr 20 '18 at 7:18
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    $\begingroup$ "st" stands for "stochastic" and, indeed, $X\stackrel {st}=Y$ means that the distributions of $X$ and $Y$ coincide. One also uses $X\stackrel d=Y$ to the same effect, then "d" stands for "distribution". $\endgroup$ – Did Apr 20 '18 at 7:50
  • $\begingroup$ Thank you! That makes perfect sense. $\endgroup$ – Melissa Key Apr 20 '18 at 10:43

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