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
0answers
11 views

Representing a multivariate normal with a scaled variance

I would like to model an observation to have a multivariate normal distribution but am having some trouble figuring out the linear algebra. So, let us start with a distribution that I know how to ...
0
votes
0answers
23 views

Probabilistic score vs $L^2$ norm to evaluate Gaussian Mixture Models

There seems to be (at least) two ways that one could evaluate the fit of a Gaussian Mixture Model (GMM) to a data set. First, a probabilistic score, is the log likelihood of a set of points $D$ ...
1
vote
0answers
20 views

QQ plot in Python

I generated a qq plot using the following code. I know that qq plot is used to check whether the data is distributed normally or not. My question is what do the x and y axis labels indicate in qq plot ...
1
vote
0answers
10 views

Prior for a linear transformation matrix: Matrix Normal Distribution

I have been trying to derive some conditional distribution for parameters of a linear transformation (represented as a matrix) and I had a lot of help on this thread yesterday. However, I realised I ...
1
vote
0answers
22 views

Device Comparision: Correlated or uncorrelated measurements

Background: I want to compare two devices measuring a certain characteristic on a subject. Thereto, each subject is measured once with device A and once with device B. It needs to be assumed that ...
0
votes
0answers
14 views

Estimate the conditional distribution of an latent variable?

What techniques might best illuminate the underlying conditional distribution of a latent variable and what information or assumptions would improve that illumination? For example, if we have data ...
0
votes
0answers
11 views

ANOVA: testing assumption of normality for many groups with few samples per group

Assume the following situation: we have a large number (e.g. 20) with small group sized (e.g. n = 3). I noticed that if I generate values from the uniform distribution, the residuals will look ...
0
votes
1answer
20 views

Calculating Standard Deviation when given sample size, mean difference & p value

I am trying to pool data in my meta-analysis and i need MEAN & SD. However the study has reported sample size (27), before (11.8) & after mean (11.9), and p value (0.540). I need the SD. ...
0
votes
1answer
27 views

A quiz problem on normal distribution and probability?

I was asked this question in interview. I couldnt answer this, can some one help. An investment, 16% chance to lose money on a quarter, and each quarter follows i.i.d. normal distribution. �Q: what ...
0
votes
0answers
2 views

Guassian function amplitude estimation

I have noisy 2D data from a camera that is normally distributed. I would like to estimate the parameters of this normal distribution (sigma X, sigma Y, and amplitude). What options do I have? I am ...
0
votes
1answer
36 views

Computing the conditional distribution for the mean of a Gaussian

I have the following distributional assumptions on some on my RV and model parameters: $$ y_i \sim N(\beta x_i, w_i^{-1}\Sigma_y) $$ There is a normal prior on the parameters $\beta$ as well: $$ ...
0
votes
0answers
20 views

How to calculate the expectation value of a sum of complex exponential functions with a normal distributed variable [on hold]

I'm doing magnetic resonance measurements, the signal that we measure is represented as complex numbers (in reality we measure two signals of a circular polarised electromagentic wave). I denote the ...
13
votes
2answers
354 views

Distribution of the maximum of two correlated normal variables

Say I have two standard normal random variables $X_1$ and $X_2$ that are jointly normal with correlation coefficient $r$. What is the distribution function of $\max(X_1, X_2)$?
0
votes
0answers
15 views

normalization of data points in order to make them adhere to a specified probability distribution (e.g. Normal)

I am doing some preprocessing for a computer vision task. My target is to select a few elements (pixels) containing highest scores according to a metric that I am developing. The values of this metric ...
0
votes
0answers
11 views

Choosing which distribution is most accurate

Let's say we have two samples from different normal distributions and we want to determine which distribution is most accurate relative to an ideal value. How would we evaluate which one is more ...
0
votes
0answers
31 views

How do I classify data with multiple dimensions using a gaussian classifier? [closed]

I've computed the equation inside the brackets (but not i): Features=dimensions (x,y)..R^n Ck being the covariance matrix, z being the input vector, u being the mean vector, N being the number of ...
1
vote
1answer
50 views

Is a Brownian motion non-stationary?

This Wiki-Article quotes "a Brownian motion process, is non-stationary" I dont see why this is the case? A stationary process means that the distribution of ...
0
votes
1answer
48 views

assumptions made for a normal distribution- a interview question

I was asked in my interview: What assumptions can you make? Why and when? (i.e When is it safe to assume "normal"). Can some one answer this .
0
votes
0answers
14 views

How to model shoe price distribution?

How would you model prices for shoes? Prices on shoes differentiate on color, size and on the retailer that sells them. I'm trying to come up with a distribution that I can sample. The average of ...
1
vote
0answers
34 views

Huber's M estimator for contaminated Gaussian noise

Huber discussed in this seminal paper "Robust Estimation of a Location Parameter" link that if we have some observations $x_i$ as follows: $$y_i = \theta + \nu_i, ~~i=1,\cdots,N, \tag{1}$$ where ...
0
votes
0answers
16 views

Multivariate Gaussian, rearranging means

Looking through the the matrix cookbook, a collection of matrix identities, I came across this one called "rearranging means" in the multivariate Normal distribution (Sec. 8.1.5 or Eq. #356, also ...
0
votes
0answers
13 views

Activation functions for z-score data

I'm currently using a neural network to try modeling z-score data. Because of the 68, 95, 99.7 rule, I naturally want to have an activation function that has the characteristics that Starts to ...
0
votes
0answers
32 views

Multivariate normality in Discriminant Analysis when using dummy variables

I've studied statistics now for almost two years and I'm starting to believe I have missed something very fundamental. I'm doing discriminant analysis where, as I understand it, I can use dummy ...
0
votes
0answers
9 views

Creating A weighted Scorecard using Stats

Im new to forum and have tried reading some articles to solve my problem but had trouble understanding some of it and others might not have been completely relevant. Below I will outline my problem ...
0
votes
0answers
26 views

Reducing the amount of data by extracting a representative sample of my population

I have 6 B&W images representing different wavelengths (i.e. Landsat bands) of the Alta Valtellina (Italy). I extracted from the images only the areas of bare soil. Now, I want to perform a PCA on ...
0
votes
0answers
43 views

How do you interpret Kolmogorov-Smirnov Test results in R?

I'm using 50,000 values of data. I can't perform a K.Wallis test in R because my data amount is bigger than 5000. Therefore I considered to use Kolmogorov-Smirnov test. I guess that my data follows a ...
0
votes
0answers
21 views

Example of parametric and non-parametric method

I have not understood this example from wikipedia. Suppose we have a sample of 99 test scores with a mean of 100 and a standard deviation of 1. If we assume all 99 test scores are random samples ...
2
votes
1answer
33 views

Normal distribution area vs. exponential distribution area

Why is the area to the left of the mean different in normal distributions comparatively to exponential distributions? I understand that in normal distributions area is allocated symmetrically on ...
0
votes
0answers
24 views

Finding a confidence interval for observations being outliers

Suppose I have a sample with sample size $N$ that is obtained experimentally, e.g. I have counted the number of birds at a certain location at a certain time. Now suppose that the sample (the number ...
0
votes
1answer
31 views

Given a sample of size n from a normal distribution, estimate the probability of picking a value larger than X from this distribution

Say I picked 10 random samples from a normal distribution with unknown parameters: 1.7, 2.6, 3.0, 4.4, 1.6, 2.1, 2.4, 2.7, 5.2, 3.3 What is the probability that I will pick a value larger than ...
4
votes
1answer
39 views

Accounting for non normality

I have a random variable, supposedly from a Bernoulli distribution, and I want to do some tests on its mean. I'd like to assume that the sample mean is normally distributed, but I'm not sure how ...
1
vote
0answers
15 views

asymptotic distribution of outlier detection tests

What is the asymptotic distribution of Dixon and Grubbs discordancy test statistics, if the data are from a normal distribution (such as simulated data, perhaps).
0
votes
0answers
16 views

Why this function (smooth monotonic) keeps the gaussian aspect?

Do you know why the function below "keeps the normality" when x is normal? (positive, resulting from a binomial distributed and by the Central Limit Theorem) $X \sim N(E(X) >> 0,Var(X))$ ...
12
votes
1answer
360 views

Same Mean, Different Variance

Suppose you have eight runners run a race; the distribution of their individual run times is Normal and each has mean $11$ seconds, say. The standard deviation of runner one is the smallest, two the ...
3
votes
3answers
173 views

Find distribution and transform to normal distribution

I have data that describes how often an event takes place during one hour ("number per hour", nph) and how long the events last ("duration in seconds per hour", dph). This is the original data: ...
1
vote
1answer
36 views

How to change peak height in Excel

I have a normal distributed bell curve (created in excel). I want to change the data so that the peak of the curve is reduced and the edges of the curve are increased, without changing the overall ...
2
votes
0answers
15 views

Proving the given quadratic form is chi-squared $k$

Suppose $\underline{X}$ is an $m$-dimensional vector following multivariate Normal distribution i.e. $\underline{X}$~$N_m(\underline{\mu},\Sigma)$ where $\Sigma$ is positive definite. Let $B$ be a ...
5
votes
1answer
94 views

Distribution of “normalised” Gaussian random variables

Let $X_1, \dots, X_n$ be independent normally distributed random variables. What is the distribution of: $$ Y_i = \frac{X_i}{\mathrm{stdDev}(X_1, \dots, X_n)}, $$ where $\mathrm{stdDev}(X_1, \dots, ...
0
votes
0answers
50 views

mean imputation justification in Gaussian Discriminant

Assume that using a Gaussian discriminant for a binary classification problem, I want to classify a new data $X = x_1, x_2,...x_n$ but the corresponding value of $x_n$ is missing. I have to prove that ...
0
votes
0answers
7 views

Estimating the covariance matrix in LDA ESL

I am reading Elements of Statistical Learning on LDA. On page 109, it talks about how we need to estimate parameters for Gaussian distribution. But why do we use this estimate for the covariance ...
2
votes
1answer
27 views

Approximation of “translated and scaled” Poisson distribution by normal distribution?

If I have a random variable $Y=a(\frac{b}{c}+\frac{X}{c})$, where $a,b,c$ are all integers and $X$ is Poisson distributed with a mean which is large enough to be approximated by the normal ...
2
votes
1answer
19 views

Jitter/Variation in normal distribution

I am studying frame delay variation (FDV) in packet networks. I will explain what that is (or what I interpret it to be) in more detail in a second. I'm assuming the time difference between two ...
7
votes
1answer
581 views

Which converges faster, mean or median?

If I draw i.i.d. variables from N(0,1), will the mean or the median converge faster? How much faster? To be more specific, let $x_1, x_2, \ldots $ be a sequence of i.i.d. variables drawn from ...
2
votes
0answers
13 views

Spectral norm of a sparse Gaussian matrix

Suppose $G$ is an $m \times n$ matrix such that each entry of $G$ is a standard normal variable. We know that the spectral norm of $G$ scales as $\sqrt m + \sqrt n$. Now, given a set of indices $S$ ...
6
votes
2answers
91 views

How to Transform a Folded Normal Distribution into a Gamma Distribution?

Let the random variable $X$ have the folded Normal pdf $$f(x)=\frac{2}{\sqrt{2\pi}}e^{\frac{-x^2}{2}}$$ with $0\lt x \lt \infty$. What is the transformation $g(X)=Y$ and values of $\alpha$ and ...
0
votes
1answer
18 views

How to use a reference table to determin if a sample mean is consistent with population

I have a sample of people (n=36) with a mean cholesterol level of 4.1. The reference table states that the normally distributed population has values between 3.2 and 6.2 (95% confidence interval). ...
0
votes
0answers
14 views

Efficient generation of graph structured correlated random variables via MCMC/Gibbs

Sometime back I had asked this question about generating correlated random draws based on the correlation structure given by a graph. Link Here The solution there requires to create $n\times n$ ...
-3
votes
1answer
77 views

Calculating mean and variance of normal distribution restricted to interval

If one set a lower and an upper limit on the normal density, is it statistically valid to calculate the mean and Standard deviation of that normal variate. If yes, how can we do that in R? In a more ...
1
vote
0answers
13 views

How to Deal with Peaks and Valleys on Scale Data

I've got a questionnaire/scale from 0-8, let's say it's a mood scale (0 = no depression, 8 = most depressed ever felt), subjects fill in a bubble along the scale, but the numbers aren't there, only ...
2
votes
1answer
33 views

What is the nature of the normality assumption in models for longitudinal data?

I'm working on a longitudinal dataset to which I've been fitting non-linear mixed effects model in R. Regarding normality, I have a few questions: Can I assume that a longitudinal data is normally ...