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# Questions tagged [approximation]

Approximations to distributions, functions, or other mathematical objects. To approximate something means to find some representation of it which is simpler in some respect, but not exact.

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47 views

### Frequency of N Independent Events

I'm attempting to implement a numerical approximation to assess the frequency of outcomes given $N$ independent random variables. There is a slight twist however, each $N$ has a weight, Each variable ...
149 views

### Approximated relation between the estimated coefficient of a regression using and not using log transformed outcomes

Consider the two regression equations: \begin{align} Y &= \alpha+\beta X+\varepsilon \\ \log Y &= \gamma+\delta X+\eta \end{align} Is there a "simple" approximated relation between the ...
164 views

The following is from Section 2.2 of the Auto-Encoding Variational Bayes paper, It says the gradient of the lower bound w.r.t $\phi$ is a bit problematic because the Monte Carlo estimator exhibits ...
235 views

### Double integral in the context of a bivariate normal distribution

This question is relevant to bivariate normal distribution. I figured out most of the steps but am currently stuck on finding the closed form of a double integral. Let $x$ and $y$ be of a bivariate ...
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### Ratio in a random subset without replacement

This function returns a random proportion. It appears normally distributed with mean $a/(a+b)$. What is its approximate variance? ...
2k views

### Why does the reconstruction error of truncated SVD equal the sum of squared singular values?

I saw this formula in a textbook: squared Frobenius norm of the original matrix $\mathbf X$ minus its truncated SVD $\mathbf X_k$ (which can be seen as the approximation error) equals the sum of ...
35 views

### Other types of mean error

Let $\tilde f$ be an approximation of the function $f(x) = \arccos(x)$. I'm using MATLAB to figure out how good this approximation is by calculating a mean error. My first idea was to use this formula ...
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### Digits that are insignificant by virtue of representing extremely small quantities within a much larger quantity: what are they called?

In computer science, sometimes we can measure run-times with high accuracy. As a hypothetical scenario, suppose a computation takes a week to run and we can measure the run-time accurate to the ...
256 views

### 68–95–99.7 rule for binomial distribution?

What I want to calculate is the probability that the size $k'$ of an intersection of two subgroups with sizes $n$ and $K$ that have been randomly selected from a group with size $N$ that is smaller ...
5k views

### normal approximation to the binomial distribution: why np>5?

Nearly every text book which discusses the normal approximation to the binomial distribution mentions the rule of thumb that the approximation can be used if $np\geq5$ and $n(1-p)\geq 5$. Some books ...
454 views