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4 questions
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Number of simulated statistics more extreme than most extreme real data statistic
I have a distribution of $n_{obs}$ "real" data observations drawn from a normal distribution $X \sim N(\mu,\sigma^2)$, and a number $Q$ of simulated realizations of the same distribution, ...
2
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0
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Maximum Uncertainty in Normal Distribution
While reading Goodfellow's Deep Learning Book, I came across the below fact about Normal Distribution. I am not sure I have understood what led to this conclusion, Can someone help with it?
"Out ...
1
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1
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How to expand $\text{erf}\bigg(\frac{(ax-b)}{\sqrt{2}}\bigg) = \text{erf}\bigg(\frac{ax}{\sqrt{2}}\bigg) + \text{some_value}$?
The error function is defined as, $$\text{erf}\bigg(\frac{(ax-b)}{\sqrt{2}}\bigg) = \frac{2}{\sqrt{\pi}}\int_{0}^{\frac{(ax-b)}{\sqrt{2}}} e^{-t^{2}/2}dt$$. My question is how to expand the above ...
2
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1
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How to estimate true value and 95% bands when distribution is asymmetrical?
I have a set of results of independent measurements of some physical quantity. As an example I give here real expermental data on methanol refractive index at 25 degrees Celsius published in ...