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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, ...
user406833's user avatar
2 votes
0 answers
108 views

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 ...
umesh's user avatar
  • 51
1 vote
1 answer
34 views

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 ...
score324's user avatar
  • 335
2 votes
1 answer
2k views

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 ...
Alexey Popkov's user avatar