**3.384 normal-distribution questions.**

Suppose I have two ways of approximating cumulative normal probability and I want to compare whether the two methods are equivalent.
The most obvious way to go about it would be to have a bunch of ...

What is the best method for testing for normality? I have a smaller data set today (30 in each group) and on the histograms none of them look normally distributed at all, whereas with the skewness ...

I have understood that the Normal distribution may be motivated by considering the Binomial distribution for large N. I wished to create a geogebra file but encountered a problem I'd not thought of ...

I need to estimate as fast and accurately as possible the differential entropy of a mixture of $K$ multivariate Gaussians:
$$
\mathcal{H}[q] = -\sum_{k=1}^K w_k \int q_k(\textbf{x}) \log \left[\sum_{...

Given
$\textbf{x}=[x_1 x_2 ... x_n]^T$ where $\textbf{x} \in \{ 0, a_1, a_2, a_3 \}^n, a_i \in \mathbb{C}$ and $\textbf{z} = \left\{z_1,z_2,\dots,z_n \right\}$ where $z_i \sim N(0,\sigma^2)$ is a ...

For a loadtest I have to figure meaningful numbers for the maximum number of requests per hour and minute. The only thing I have is the number of requests per working day (which is a timeframe of 14 ...

Consider the mean estimator
$$\hat{\mu}(\lambda) = \lambda \frac{1}{n}\sum_{i = 1}^nY_i $$
(for $n$ iid Gaussian variates $Y_i$). After calculating the bias and the variance of this estimator, I ...

(A cross post after finding more appropriate tags here.)
My question is on Bayesian inference of partitioned multivariate Gaussian. To make things easier, suppose there is a 2-dimensional Gaussian,
$$...

I am coding various normal random variable generators, one of them being the acceptance rejection method:
...

I want to better understand the step for calculating the message from the game factor $h_{g}$ down to the difference variable $d_g$ on the TrueSkill factor. Such message is shown in the Rasmussen's ...

I'm doing a sports-related analysis about comparing regular-season performance versus playoff performance, in particular which teams tend to do better during the playoffs. Thus, I'm making a "regular ...

Suppose there is a left-censored normal distribution, and we know there is a total of $m$ samples, for which we know $n$ of them. I am trying to estimate the mean and variance of the underlying normal ...

It's been a long time since basic statistics. I have a financial time-series that exhibits exponential growth.
Before I standardize, do I have to make the time-series stationary?
Before I ...

I have these two Gaussian distributions: fX1 ~ N (10, 12)12 is the variance and not standard deviation
...

All the time I see examples of the normal/Gaussian distribution with continuous random variables. So my question is do all continuous random variables have a Gaussian distribution?

I try the shapiro.test for my transformed dataset (logarithm). I obtain p value 0,0001207. I try to draw the graph of distribution and obtain this graph (I attached).
For you, do I have a normal ...

I want to add noise to a given time series of data. The noise is to be generated using a distribution technique. For example for an interval of 10 min I have 60 entries which sum upto say 13643Kw. ...

Suppose $z\sim N(0,1)$ and $x\sim N(\gamma z, 1)$, where $\gamma$ is a known sensitivity parameter. That is, $x=z+\epsilon, \epsilon \sim N(0,1)$ where $\epsilon$ is exogenous.
Further, suppose there'...

Let's say I have a pencil factory. I don't mind if my pencils are too short, but it's important they're not too long.
My Quality Control department measure each pencil, and their measurement will be ...

Some values have a normal distribution with mean .0276. What standard deviation is required so that 98% of values are between .0275 and .0278?
What I'm confused with is how to calculate the standard ...

I know that a sum of RVs bernoulli distributed with the same parameter $p$ may be approximated with a normal distribution.
My question is whether a single bernoulli RV may be approximated with a ...

For example, we always assumed that the data or signal error is a Gaussian distribution? why?
I have asked this question on stackoverflow, the link: https://stackoverflow.com/questions/12616406/...

It should be a simple statistic question:
X,Y ~ Phi(0,1) (normal distribution). What is the probability that X > 5*Y
Anyone can teach me how to do it?

If $x$ and $y$ are independent and normally distributed:$$x\sim N(\mu_x,\sigma_x)$$
$$y\sim N(\mu_y,\sigma_y)$$
and $r$ is a random variable with the following relationship to $x$ and $y$
$$r = \sqrt{...

I have a set of data of 5 members. based on some previous questions , I was expecting to see where my actual points are located on the graph. in my case I see the theoretical but not my points.
just ...

I'm given a subspace $V$ and a set of $n$ corrupted observations $\tilde{x}_1 = x_1 +\epsilon_1,...,\tilde{x}_n = x_n + \epsilon_n \in \mathbb{R}^D$. Assume $D$ is large and that $\epsilon_i \sim N(0, ...

Is the Central Limit theorem still applicable if we consider a sum of independent but different random variables? (Each with finite mean and variance)
Is there some theorems about this ?

My study is related to the visual attractiveness of route-plans in a logistics context. In practice, route-plans are rejected based on the fact that they "do not look nice". I have conducted an ...

I am trying to simulate data that is correlated to varying degrees. However, the data itself will have a degree of autocorrelation as well. I can get the first part of the problem with mvrnorm ...

Given $n$ independent observations $X_1,X_2,\ldots X_n\sim\mathcal{N}(\mu,\sigma^2)$, where both the variance and the mean are unknown. How can I write down a confidence interval for $\mu+c\sigma$, ...

I have plotted 8 curves using a log-link Gaussian model, y=ax exp(bx)+ϵ, for my data. I couldn't find a way extrapolate the maximum (x,y) from each of the fitted curves, of which I intend to use for ...

As I dig deeper than surface level in probability I'm starting to ask more questions I never thought about before.
There are a bunch of intertwined concepts that are quickly becoming confused in my ...

I am looking to generate a synthetic set of data. For clarity I will use a simple example and then elaborate.
Suppose that I would like to create a set of data concerning the color and size of a ...

What is the distribution of $\min\{0, X\}$ when $X$ follows some general normal distribution?

I understand that the normal distribution is undefined if the standard deviation is zero, but I need to handle the case where all values are equal in a computer algorithm. The following method must ...

I'm looking for a way of correcting a linear fit through data.
The scenario is the following:
In red you have data points, they are based on uniformly distributed points on the black straight line ...

from the following log-normal fitting function (https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html), I get the parameters [s, loc and scale]. How can I use them to get the μ ...

I would like to discuss and ask a question regarding the Fourier transform of a Gaussian process, if it makes sense.
For that purpose, let me describe the following situation.
Let $z(s)$ be a ...

I have read somewhere in the literature that the Shapiro–Wilk test is considered to be the best normality test because for a given significance level, $\alpha$, the probability of rejecting the null ...

If $X$ and $Y$ are normally distributed but correlated variables, what can we say about the distributions of $A = X+Y$ and $B = X-Y$?
Are $A$ and $B$ correlated? Can we prove or otherwise with a ...

Suppose I have a data set which has a nice Gaussian distribution f(x), then I can "summarize" as
Mean{f(x)} +- Std{f(x)}
Where std stands for standard deviation. However, If my data does not look ...

Classic A/B test suppose that there are two independent experiments, each with $n_1$ and $n_2$ observations, for which we are interested in an event following a binomial distribution $\mathcal{B}(n_1,...

I am currently working with a set of samples of stable isotopic concentrations obtained from a group of individuals.
I am trying to process this data through a glmm() from the package lme4 to ...

I'm watching a pool match and at the start of the first game the person next to me says
"I think the chance of player A winning the first game is $.700$. If he wins that I think the chance of him ...

I'm not sure how to implement this architecture. I'm following this thesis http://www.cs.toronto.edu/~ndjaitly/Jaitly_Navdeep_201411_PhD_thesis.pdf (pag 17-19) or this paper http://www.cs.toronto.edu/~...

I have done a simulation with 1 million runs on Matlab. I have got a histogram for this. Using Matlab command hist(X), (where X is the 1 million samples as results ...

This is Exercise 3 in Section 6.3 of Probability and Statistics, 4th edition, by DeGroot and Schervish:
Suppose that the distribution of the number of defects on any given bolt of cloth is the ...

This answer notes that if a programming language/libraries provide a procedure that returns random samples from a standard normal distribution, we can generate samples from another normal distribution ...

Let's say that I have a 2d map, and I would like to explore around my house. Drawing samples from a bivariate gaussian centered at the x, y location of my house makes sense, as I don't want to stray ...

I analysing time-series to see the range of an asset. I have data for GBPUSD so i could only analyze this so far.
I have used both empirical rule and percentile. Of course they give different ...

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