# 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.

474 questions
Filter by
Sorted by
Tagged with
60 views

### Continuity correction in a 2 proportion test, with different sample sizes

In a test of 2 proportions (binomial -> Normal), when the sample sizes are different, what does a continuity correction look like? Usually, in a 1 sample test, we would divide by $n$ (sample size) ...
10 views

87 views

### Universal approximation theorem for neural networks reference

On Wikipedia, a nice theorem is given: However, I can not find the stated theorem in the given references. So where is the stated theorem from?
• 158
1 vote
12 views

### Getting extremely poor accuracy while doing function approximation using a neural networks in PyTorch [duplicate]

I have been given a task to approximate the function 5x^3 - 10x^2 - 5x - 9 using a neural network in pytorch. The training data is the set of integers in the range [-100,100] and I have to test the ...
• 11
22 views

### Approximation for a correlation matrix

I have a cross-correlation matrix of some parameter for each time period. E.g. expected economy growth for each months in the future, i.e. growth for Apr 2014, May 2014, ...., Dec 2018, and ...
75 views

### What paper did Hall suggest the queuing rule of thumb $s \geq \max ( 1, \rho + \sqrt{\rho})$?

According to this site: Hall (1991) cited an argument of his previous paper that operation research profession could and should be more scientific and less mathematical. In fact, Hall also suggested ...
• 8,784
58 views

### Montecarlo Confidence Interval of T distribution

Suppose: $$x|\sigma^2 \sim \mathcal{N}(x; \mu, \sigma^2) \; \; st. \; \; \sigma^2 \sim \mathcal{X}^{-2}(\sigma^2; \psi, v)$$ where $\mathcal{X}^{-2}$ is the inverse ...
• 301
1 vote
75 views

### Taylor approximation for function of a random variable [closed]

There is a function $f$ whose domain is the space of CDFs on $\mathbb{R}_+$ and whose range is $[0,1]$, e.g. $f$ maps a CDF on to a real number. Further, $f$ is continuous, increasing with respect to ...
• 111
83 views

### Moments and PDF of solution to random quadratic equation

Consider the following random quadratic equation, $$x^2 + Z x + Y = 0,$$ where, $$\begin{gathered} Z \sim \mathcal{N}(\mu_Z,\sigma_Z), \qquad Y \sim \mathcal{N}(\mu_Y,\sigma_Y). \end{gathered}$$ ...
• 93
1 vote
48 views

### Little's Law + Kingman's Formula --> Approximation of Expected Length of G/G/1?

Little's Law gives us $$\mathbb{E}[L] = \lambda \mathbb{E}[W]$$ where $L$ is the number of customers in the queue + being served $\lambda$ is the arrival rate $\mu$ is the service rate $W$ is the ...
• 8,784
127 views

### Diffrence in logs vs. a % changes in econometrics: why is the dif log approvimation almost always used when the exact quantity is easily available?

I have observed that in econometrics work people almost always use the difference in logs rather than the actual percentage change. This makes no sense to me. I understand that the difference in logs ...
• 3,117
45 views

### Is there a heavy traffic approximation for percent under benchmark?

Suppose I have an waitlist of patients waiting to be served. Each patient has a benchmark number of days that the service should be completed by as a goal (not a hard constraint of the modelling). ...
• 8,784
90 views

### Approximating the distribution of the product of iid beta variates

Background I am interested in the distribution of $$\theta_0=1-\prod_{i=1}^n(1-\theta_i)$$ where the $\theta_{i>0}$ are iid beta random variates: $$\theta_{i>0}\sim\text{Beta}(\alpha,\beta)$$ In ...
• 1,504
79 views

### Approximating the standard normal density with the logistic density: How to numerically optimize $\infty$-norm?

Let's say that we want to use the logistic distribution as an approximation to the standard normal density. As the location parameter of the logistic distribution is $0$, the scale parameter $s$ is ...
• 30.7k
87 views

• 141
62 views

### Extract the functional mapping between input and output from a machine learning model

A lot of ML models, such as neural networks, are Universal Function Approximators. But when evaluating ML models, we use usually metrics, such as MSE or accuracy, to assess the performance of a ML ...
I have a set $S$ = {$e_1,e_2,..e_{400}$} of 400 elements and a non-linear function $f:2^{(S)}\to[0,1]$ that takes a subset of $S$ and returns a real number in $[0,1]$. I want to compute the subset for ...