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.

learn more… | top users | synonyms (2)

0
votes
1answer
16 views

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

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
votes
2answers
37 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 ...
0
votes
0answers
5 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
votes
1answer
28 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 ...
6
votes
1answer
179 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 ...
0
votes
1answer
12 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 ...
1
vote
0answers
14 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 ...
0
votes
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 ...
0
votes
1answer
19 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 ...
0
votes
1answer
20 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
vote
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
votes
1answer
55 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 ...
1
vote
1answer
30 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, ...
0
votes
2answers
46 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) = ...
0
votes
0answers
9 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 ...
0
votes
0answers
18 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
votes
3answers
183 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 ...
-1
votes
0answers
19 views

Contour of bivariate normal in r [closed]

How to sketch constant-density contour that contain 95% of the probability, when population means are zero, variance of two variables are 2 with covariance -0.2 and correlation coefficient is -0.5.
2
votes
1answer
71 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 ...
0
votes
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 ...
-1
votes
1answer
72 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 ...
1
vote
1answer
18 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
votes
0answers
32 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 ...
0
votes
0answers
15 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
0
votes
0answers
8 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 ...
1
vote
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 ...
0
votes
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
votes
1answer
43 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
votes
2answers
100 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
votes
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 ...
0
votes
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 ...
0
votes
1answer
39 views

Normality test for large samples

So I working on a programming assignment that uses multiple algorithms to solve the floodit game. I have taken some of my data that I have collected thus far. I did a shapiro test: ...
0
votes
2answers
42 views

How to show that a dataset does not contain significant outliers?

I have largish dataset: there is 200 variables and 100 samples. How could I show that the dataset does not contain any significant outliers? All variables have the same unit (millimeters) and have ...
0
votes
1answer
14 views

Confidence Interval for 5% Lower Limit

For a normal distribution with a mean of X, and a standard deviation of SD, the 5% lower limit of the population is computed as X-1.645*SD. Meaning, 5% of the population will not reach that level. ...
0
votes
0answers
8 views

R gplot for normal distribution - add data to graph [migrated]

I'm trying add to my plot some data that will facilitate users. My distribution graph comes from this code: ...
2
votes
2answers
37 views

Z-score in the analysis of data

I am being provided z-scores of dependent and independent variables. I was checking if it can analyzed as such as raw data?
1
vote
0answers
27 views

Correlation between two quadratic forms of Gaussian random vectors

I want to approximately calculate the correlation between two quadratic forms of two Gaussian random vecotrs (of course these are in fact non-Gaussian densities). Does anyone know the derivation of ...
0
votes
2answers
40 views

Going from a normal distribution to a standard normal distribution with a change of variable

If $X$ follows a normal distribution with parameters $\mu$ and $\sigma^2$ show that $Z = (X- \mu)/\sigma$ follows a standard normal distribution. This doesn't seem to intuitive to me. We shift $X$ so ...
1
vote
1answer
31 views

Best way to define where the data is no longer normally distributed

I thought I'd first give a brief description of what my data is so that it's easier to understand what my problem is. I have a dataset which goes as follows:- binned mass differences of compounds vs ...
0
votes
1answer
349 views

Why probability distribution function gives “~.40” probability when it should have been 1.0? [duplicate]

I am following code given here- http://www.bigdataexaminer.com/how-to-implement-these-5-powerful-probability-distributions-in-python/ Under "Normal Distribution" section, the graph peaks at .40 when ...
1
vote
0answers
28 views

Gaussian random variables [duplicate]

Can some one help me point in the right direction or point to some resources that will help me prove that sum of two jointly distributed Gaussian r.v. with a given correlation coefficient is also a ...
2
votes
0answers
27 views

Confidence Intervals of a Given Width

I'm working through some questions on confidence intervals. My answer doesn't match the book, but the book's answer was a number I had a few steps before the end. I have ten numbers which are a ...
1
vote
1answer
46 views

Normal distribution. Find the average

In a large group of patients, cholesterol level approximates a normal distribution N(μ, σ). Observed that 20% of the members of this group have a cholesterol level of less than 117.7mg/100ml and 8% ...
1
vote
2answers
44 views

Does this regression diagnostic plot mean my data is invalid, and if so how should I go about fixing it?

I am doing a project on cloud cover and cosmic rays and have undertaken a regression model in R. Above is the regression diagnostic plot and from the QQ plot I can see that the tails are skewed, ...
0
votes
2answers
48 views

How to deal with 'cut-off' selection bias/sampling bias? (truncated distribution)

In short When measuring an outcome with a normal distribution, but whos mean is below the detection threshold, can you still make statements about differences between populations? Example Say I ...
0
votes
0answers
27 views

not normally distibuted residuals

I have made an linear regression model using stata. I have made my model diagnostics - predict y, predict (rstudent) residuals. When I control the residuals for normality by a Q-Q plot, it is ...
0
votes
0answers
51 views

Does stationary data need to be normal?

So I already ran some tests to make my data stationary. Differencing and box-cox transformation in particular. According to the augmented-dickey fuller test, after performing the above mentioned ...
1
vote
1answer
29 views

What is the nonlinear transformation assumed by the gaussian (rbf) kernel?

A common kernel choice is the gaussian kernel: $ k(x,x^{'}) = \exp \big( -\frac{1}{2\sigma^2}\| x - x^{'} \|^2 \big)$ This implies a transformation on $x$, and equally on $x^{'}$. What is it?
0
votes
0answers
25 views

Can near zeros in precision matrix be treated as zeros?

A zero entry in the precision matrix (the inverse of the covariance matrix) means the corresponding variables are indepenent given all the other variables. For real-world data samples, when is an ...
0
votes
0answers
7 views

Stability precision matrix under small changes in covariance

I am trying to understand how the precision matrix changes under the influence of small changes in the covariance matrix. I have several similar datasets: the differences in standard deviation for the ...