# 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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### Normal approximation to the Poisson distribution

Here in Wikipedia it says: For sufficiently large values of $λ$, (say $λ>1000$), the normal distribution with mean $λ$ and variance $λ$ (standard deviation $\sqrt{\lambda}$), is an excellent ...
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### Estimate probability of event using moments of a distribution or a Taylor expansion involving the moments

Let's say we have four moments $(\mu_1, \mu_2, \mu_3, \mu_4)$ of a probabilty distribution of a random variable $X$ and the goal is to get the probability $\rm{P}(X \leq t)$ for a certain value of $t$....
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### Normal approximation to the binomial distribution

I am having trouble getting to the bottom of this concept for two types of questions (hw is already passed, but I have a test this week and would like to do better). Hopefully someone can help me get ...
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### How many times do I have to roll a dice to get six six times in a row? [duplicate]

I wonder if there's any exact way to find out these two things about six-sided dice: How many throws would be necessary to get six times the same number (let's say six) in a row? What's the ...
582 views

### maximum gap between order statistics of normally distributed random variables [closed]

I am currently working on a not-that-easy problem involving order statistics. As I am unsure as to how I could solve it, I thought it might already possess a solution. So here I am, my questions is: ...
117 views

### help with expectation propagation: updating factors

I have been trying unsuccessfully for a while to understand and setup an inference problem and use EP with it. I have tried to extract a simple case to highlight he issue. I hope someone will be kind ...
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### Approximation of Cauchy distribution

I have a ratio of two random, (dependent or independent) normally distributed variables. Knowing that the resulting Cauchy-distribution does not produce any moments. May I ask: Is there an ...
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### Arbitrary function approximation in one dimension

Suppose we have some arbitrary function $f: X \mapsto Y, X \in \mathbb{R}, Y \in [0, 1]$. It may be smooth but it may not. I am looking for some way to approximate this function given samples drawn ...
264 views

### Expectation of the softmax transform for Gaussian multivariate variables

Prelims In the article Sequential updating of conditional probabilities on directed graphical structures by Spiegelhalter and Lauritzen they give an approximation to the expectation of a logistic ...
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### Approximate distribution of normal squared

I am studying for a test, one section of which will cover the delta method. This problem came from that section: Let $X\sim N(\mu,n^{-1})$. Find an approximate distribution of $X^2$. (It also asks ...
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### Results on continuity corrections

For me, the first thing that comes to mind when I come across the term continuity correction is that when $X\sim\mathrm{Bin}(n,p)$, one approximates $\Pr(X\le x)=\Pr(X<x)$ by $\Pr(Y<x+1/2)$ ...
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### code Welch's t-test in C++ using approximations for student's t values

I need to code a Welch's t-test between two populations in C++ without using external libraries like, for example, boost. I know that given my two populations of size $N_1$ and $N_2$, I can calculate ...
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### How to approximate Bayes Factor?

I am searching for a computationally simple way to approximate a Bayes Factor. Currently, I'm using an approach which seems pretty logical to me but I would still be interested to know if this is ...
I've been told in my current textbook that for approximation of the exact distribution by means of $X^2$ or $G^2$ the expected frequencies have to be $\ge 5$. The book says that the approximation ...