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Timeline for Which distribution do I get?

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Jan 13, 2015 at 19:42 comment added Glen_b Yes, I think you have a scaled non-central t.
Jan 13, 2015 at 19:41 history edited Glen_b CC BY-SA 3.0
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Jan 13, 2015 at 19:40 comment added John M You are right. I didn't notice it. So $\mu$ is the non-centrality parameter. The problem is that now I can't lead back the formula to the general definition of a non-central Student's t-distribution as $T=\frac{Z+\mu}{\sqrt{\frac{V}{v}}}$ where $Z$ is a standard normal and $V$ is a Chis-squared with $v$ degrees of freedom, according to this definition. Where do I put $\sqrt{\frac{\beta}{\alpha}}$? Is it a generalization of the non-central student's t? Thank you.
Jan 13, 2015 at 19:29 vote accept John M
Jan 13, 2015 at 19:26 history edited Glen_b CC BY-SA 3.0
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Jan 13, 2015 at 19:19 history answered Glen_b CC BY-SA 3.0