The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is often used as a reference against which other distributions are compared.

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Bayesian multivariate extrapolation

I'm not sure "Bayesian multivariate extrapolation " is the right formulation of what I want to do but here is my problem: I have a set of observations in a state $k$ (having a multivariate Gaussian ...
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18 views

How to fit intensity peaks from a image?

I have a image - that I can convert to a txt/table with all intensities. In this image, several regions show higher intensity, i.e. a peak. A peak may be stored in a 10x10 matrix with rows and colums ...
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1answer
19 views

Finding vectors with an extreme component

I'm looking for a function that measures if a vector component dominates all the rest. Let $$ \mathbf{v} = [v_1, v_2, \ldots, v_n] $$ and assume that it is L2 normalized, $|\mathbf{v}|_2 = ...
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1answer
42 views

Convergence of EM for Mixture of Gaussians

Is the Mixture of Gaussians model (an example of latent class analysis) gauranteed to converge on a viable solution even on Unimodal data using the Expectation Maximization algorithm to estimate the ...
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0answers
27 views

How to plot the cumulative distribution function of std normal dist/smooth curve, step functions [on hold]

Look for “pnorm” and “pbinom” in help. Use these commands to plot the cumulative distribution function of the standard normal distribution (of parameters 0,1) and of binomial distributions of ...
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1answer
49 views

General formula for finding covariance of monomials of multivariate random variables

Suppose that we have independent random variables $X_1,X_2,X_3$ which are gaussian multivariate distributed with a mean of zero vector and a diagonal covariance matrix. $X=[X_1,X_2,X_3] \tilde{} N(0, ...
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2answers
25 views

Expected Value Normal Distribution over an interval

The mean of a normal distribution is theta and variance is 1. I know that E(X)=theta. Then, if I compute the integral I would use to find E(X) but instead I only take the integral from (-a,a). How ...
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0answers
24 views

Question about histrogram in R-studio [on hold]

Here is my code in R-studio hist(NPV, breaks=40, main="Frequency Distribution of NPV", xlab="Net Present Value (NPV)", col="blue", ylim=c(0,1000)) I have some questions about histogram in R-studio ...
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3answers
471 views

Why are these file sizes not normally distributed?

I have saved 10,000 webcam images and tallied their lengths. The lighting conditions were constant throughout the recording time. The probability distribution is shown here, with my best efforts at ...
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1answer
35 views

Is my Interpretation of this statistical distribution correct? [closed]

The torque of shld flx action was between 8Nm to 10NM for 10% of the time Is my interpretation correct? If so how do I determine torque for one of the 19 activities?
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7 views

Average-to-average comparison with non normal response variable and dependent explanatory variable

I would like to compare the average expression of a gene in three different brain regions of a mammal (see the table below). Unfortunately, I had only 11 mammals to calculate each average. Moreover ...
2
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1answer
49 views

I want to take a decision on two gaussian distributions, what approach can I take?

I observe a one dimensional random source, which could be any of two Gaussian distributions with a different set of parameters that do not change over time. They have a the same variance and a ...
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0answers
26 views

An example for Gaussian Process: Singular covariance matrix?

I follow Christopher Bishop's book "Pattern Recognition and Machine Learning" and I am studying the section on Gaussian Processes. As an introduction, a simple model is given with the following ...
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0answers
20 views

scale & why normality does not matter

So I was looking at the world happiness report 2013. In most of their questions they used "0 to 10 end-labelled scale". So ya, basically "0, 1, 2,.., 9, 10". I understand that these kind of scale data ...
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1answer
25 views

How to apply the Central Limit Theorem applied to non negative variables?

My teacher explained the Central Limit Theorem and provided some examples. He told us that even if we don't have a normally distriuted variable, if we are working with sample means we can consider ...
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0answers
17 views

Plotting a 3D gaussian

I was wondering what is a good way to visualize a 3D Gaussian distributions. Suppose I have a mu(1x3) rowvector and a covar(3x3) matrix. I know I can use the basic visual formula and get the density ...
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0answers
27 views

sum of gamma and normal random variables

If $X$ has gamma distribution with mean $n/\lambda$ and $Y$ is normally distributed random variable with mean $\mu$, then what is the distribution of $Z=X+Y$?
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0answers
10 views

Normality considerations for 'Effect Size'

What are the normality considerations while calculating Effect Size (http://en.wikipedia.org/wiki/Effect_size). Can different methods for calculating effect size be classified into parametric and ...
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0answers
17 views

Deriving a probability using a more fat tailed T distribution rather than the normal distribution in Excel

I have an estimate of the central limit and standard deviation (SD) of a physical phenomenon. The SD is specifically derived from a limited sample of 12 observations. Using the 'NORMDIST' function ...
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1answer
36 views

Sum of standard normal cumulative distribution

If $N$ denotes the cumulative function for the standard normal distribution, i.e. $N(0)=0.5$, $N(0.5)=0.6915$ etc. are you able to say anything more generally about $N(a) + N(b)$ for example and also ...
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1answer
26 views

2 factorial experiment (2 by 3). DV is NOT normally distributed

I just conducted an 2 factorial experiment that has 6 conditions (2 by 3). Specifically, my design is: IV1 = prior positive information (positive in A domain vs. control vs. positive in B domain) IV2 ...
5
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2answers
51 views

Independence of Sample mean and Sample range of Normal Distribution

Let $X_1,\dots,X_n$ be i.i.d. random variables with $X_1 \sim N(\mu,\sigma^2)$. Let $\bar X =\sum_{i=1}^n X_i/n$ and $R = X_{(n)}-X_{(1)}$, where $X_{(i)}$ is the $i$ the order statistic. Show that ...
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6 views

Estimate conditional probability of connected variables

I want to model the following probability function $p(x_i|\mathcal{N}_{x_i})$, where $\mathcal{N}_{x_i}$ is the set of the variables $x_j$ conneced to $x_i$ given a specified undirected graph ...
4
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1answer
29 views

Normal with mean unequal to zero squared

It is a well-known fact that if $x_i \sim N(0,1), i = 1, \dots, n$, that then for $\nu \in \{1=1,\dots, n\}$ it holds that $\sum_{i=1}^\nu x_i^2 \sim \chi^2(\nu)$ I was wondering what now would ...
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1answer
218 views

Finding the point of maximum probability in a mixture of gaussians

I have a model that estimates probability of an object to be located in a 2d space. Using a mixture of gaussian with a set of criteria that I chose I got interesting results, and now I am faced to a ...
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1answer
19 views

Multiplying a mixture of gaussian to a prior Normal distribution

Let's say that I have a mixture of Gaussians: $$ p(\mathbf{x}) = \sum_{i=1}^K\phi_i \mathcal{N}(\boldsymbol{\mu_i,\Sigma_i}) $$ What is the correct formula if I want to multiply it to a prior ...
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21 views

log multivariate normal differentiation with VAR process

I am trying to estimate a regime switching model with an autoregressive component using the EM algorithm. The process itself can be presented this way: $$ r_{t}= A_{n \times (n+1)} \boldsymbol ...
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0answers
15 views

Summing values over a normal distribution

I am trying to estimate the data transfer requirements for an app. The app is something like a magazine: some content and a lot of readers. I am interested in the total number of bytes transferred by ...
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1answer
22 views

Find corresponding linear discriminant function in a two-class, three-dimensional classification

I am new to Patter Recognition and I am kind of stuck at a homework assignment. Any help regarding the issue will be appreciated. Thank you very much. In a two-class, three-dimensional ...
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1answer
21 views

Transformation of any normal distribution into a standardized t-distribution

What will be the transformed Mean and transformed standard deviation if any normal distribution is transformed into a standardized t-distribution? Does t force ...
1
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1answer
22 views

Clarification on Notation

I'm using Andrew Gelman's 3rd edition of Bayesian Data Analysis and am going through the exercises. For one of the exercises, he supposes that if $\theta = 1$, then $y$ has a normal distribution with ...
2
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1answer
65 views

Does linear regression assume all variables (predictors and response) to be multivariate normal? [duplicate]

I stumbled on this really nice blog. http://www.statisticssolutions.com/assumptions-of-linear-regression/ It has mentioned- "the linear regression analysis requires all variables to be multivariate ...
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1answer
38 views

Why does the amplitude, bandwidth and position of Gaussian change when data changes from positive to negative

I'm trying to fit a single Gaussian to some values in Matlab. When the values are positive, the model fits without any issues. However, when these values become negative, the r squared value changes, ...
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2answers
53 views

Dividing or subtracting : Normal PDF's? of independent random variables [closed]

There is clear rule how to multiply OR sum Normal PDF's i.e. https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables $N_1(\mu_1,\sigma^2_1) + N_2(\mu_2,\sigma^2_2) = ...
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14 views

Multivariate normal: from canonical parameterization to mean parameterization (or vice versa)

In their book (https://www.eecs.berkeley.edu/~wainwrig/Papers/WaiJor08_FTML.pdf) Wainwright and Jordan consider two types of parameterizations in the exponential family, the canonical parameterization ...
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0answers
20 views

interpret normal probability plot of residuals [duplicate]

I am looking at two normal probability plots of some residuals from a two different regressions. I am trying to make sure I fully understand what they are telling me. The first chart below appears ...
3
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3answers
209 views

How does linear regression use the normal distribution?

In linear regression, each predicted value is assumed to have been picked from a normal distribution of possible values. See below. But why is each predicted value assumed to have come from a normal ...
2
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1answer
74 views

Overlap between two normal pdfs [duplicate]

I have two normally distributed random variables (estimated from two different sets of samples), and I'd like to know how "similar" those variables are (in order to compare the sets). I had the idea ...
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0answers
10 views

distribution of GPAs

Often colleges/university opt using 'relative grading' mechanism for their students. Since we know that scores given to students on their examinations follow gaussian distribution thus grades are ...
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1answer
77 views

Slutsky's Theorem to show convergence to Standard Normal Distribution

We are given $W_n = \frac{\bar{X}-\lambda}{\sqrt{\bar{X}/{n}}}$ and need to show it converges to a standard normal distribution. EDIT: The square root in my original post did not extended over the ...
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1answer
20 views

Finding z-scores from z table relating to confidence intervals

I'm having trouble finding the proper $z$ score so that I can find the $99\%$ confidence interval. $\bar{x} = 6.01231$. with an $s$ of $1.96833$ and $n$ of $26$, and I got $2.575$ for ...
2
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0answers
34 views

Proving a “well-known” result regarding the distribution of a normally distributed random variable

In an important project work, I would like to include a "proof" of the following, but have unfortunately been unable to readily compute it myself. I am aware that this is a flaw on my part, but ...
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0answers
16 views

Jeffrey's Prior for normal distribution with mean = 0

How would I go about calculating Jeffrey's Prior for a normal distribution with mean = 0, So far I get: But then don't know where to go next. Any help much appreciated
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0answers
12 views

Self-study (Expectation Maximization on Bivariate Normal Distribution)

I see this example is also "classic", and I am attempting to understand how to approach it. I have an iid sample drawn from a bivariate normal distribution with mean vector ($\mu_1, \mu_2$) and ...
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0answers
13 views

density function of bivariate normal with almost singular correlation matrix [closed]

Let $X$ be a bivariate normal distribution with mean $[0,0]^T$ and covariance matrix \begin{pmatrix} 1&\rho\\ \rho&1 \end{pmatrix} with $\rho<1.$ I am looking for the behaviour of the ...
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1answer
48 views

How to test a hypothesis about the mean based on an assumed normal distribution?

The entrance onto a major bridge in New York City was engineered to accommodate an average of $3800$ vehicles per hour. However, a random sample of nine observations gives an average of ...
2
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1answer
44 views

Pointwise convergence of the cdf of normal random variables

For a sequence $X_1, X_2, \dots $, Let $F_n(x)$ denote the cdf of $X_n$. Suppose our sequence is $X_n \sim N(0,n) $ then for all $x$ the point-wise limit of $F_n(x)$ is $\frac{1}{2}$. How would one ...
4
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2answers
111 views

Relation between sum of Gaussian RVs and Gaussian Mixture

I know that a sum of Gaussians is Gaussian. So, how is a mixture of Gaussians different? I mean, a mixture of Gaussians is just a sum of Gaussians (where each Gaussian is multiplied by the respective ...
2
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1answer
38 views

Degenerate distribution

If $X \, \sim \, \mathcal{N}(m,\sigma^{2})$, I know that $\displaystyle \begin{bmatrix} X \\ X \end{bmatrix}$ is not a Gaussian vector since its entries are not independent. However, what can we say ...
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0answers
7 views

Probability with stacked geometric tolerances

I have two datasets for which I know the standard deviations. The data are for printing, where there are certain registration tolerances between different print layers. One dataset is the distance ...