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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24 views

Jaynes' Derivation of Herschel-Maxwell for Normal Distribution

I am reading the following paper: http://www-biba.inrialpes.fr/Jaynes/cc07s.pdf and cannot seem to figure out how Jaynes is deriving (P2) and below (specifically the log arithmetic ...
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15 views

Finding extreme values in a normal distribution [migrated]

I want to find extreme values (anything greater or less than three times standard deviation from the mean) after generating a set of random numbers using: ...
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1answer
39 views

Random Effect Model

One factor random effect model: $$y_{ij}=\mu+\tau_{i}+\epsilon_{ij}\quad i=1,2,\ldots,a; j=1,2,\ldots,n$$ where, $y_{ij}$ is the $j$th observation of $i$th treatment effect $\mu$ is the overall ...
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14 views

Interpreting R results, are the data multivariate normal?

I ran "mvn" using the "mclust" package in R using the following codes: mvn("EEE", data[,18:22], prior = NULL, warn= NULL) I am having trouble figuring out how to ...
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42 views

The Best Idea forever! [on hold]

What is your interpretation about "Source" of observations?
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3answers
102 views

Conditional Probability with Normal Distributions?

Let's say that I have $3$ independent random normal variables, $A$, $B$ and $C$. They all have a standard deviation of $17.526$, while $A$ has a mean of $143$, $B$ of $139$, and $C$ of $129$. My ...
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28 views

Computing the F-ratio under null hypothesis

Statistical model for a Completely Randomized Design: $$y_{ij}=\mu+\tau_{i}+\epsilon_{ij}\quad i=1,2,\ldots,a; j=1,2,\ldots,n$$ where, $y_{ij}$ is the $j$th observation of $i$th treatment effect ...
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1answer
47 views

What is name of this distribution and can we have 68–95–99.7 rule for it?

I have a distribution like this: What is name of this distribution? As you know we have 68–95–99.7 rule in ...
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31 views

Can I normalize Ordinal Data

I have ordinal data on three IVs ranging from 1 to 5 as below: IV1: Not at all Important - Very Important IV2: Not at all Satisfied - Very Satisfied IV3: Performs much Worse - Performs much better ...
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1answer
50 views

Variance of random variable for normal distribution

How do I find the variance for $z_n=\prod_{i=1}^n(1-k_i e^{a_i x})$ where $x$ is the random variable with a normal distribution and is the same for all $i$ (which is a subscript for time dependency ...
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2answers
41 views

Normal Distribution with random mean and standard deviation

When trying to code this in R, I'm getting very confused about what to do. Apologies if my terminology is incorrect but I would be grateful for any advice. The Problem: I have been given two normal ...
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0answers
22 views

Generating a dataset from mean, standard deviation, n and 95% CI

I have the output of a couple of Socprog models and I'd like to see if the results are statistically significant. Group A output: ...
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1answer
50 views

Correlation between two normally distributed variables

Let a~$\mathcal{N}(\mu_a,{\sigma_a}^2)$,b~$\mathcal{N}(\mu_b,{\sigma_b}^2)$ and c~$\mathcal{N}(\mu_c,{\sigma_c}^2)$. We construct two normal variables x~$a-b$ and y~$a-c$. Can we find the ...
6
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1answer
219 views

Generate random numbers following a distribution within an interval in R

I need to generate random numbers following Normal distribution within the interval $(a,b)$. I know the function rnorm(n,mean,sd) will generate random numbers ...
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2answers
79 views

Conditional expectation of $X$ given $Z = X + Y$

Suppose I have two independent normal variables $X$ and $Y$ with known mean and variance. Defining $Z = X+Y$, what is the most straightforward way to compute $\mathbb{E}\left[X|Z\right]$? I am ...
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0answers
26 views

How to apply Gaussian kernel to smooth density of points on 2D (theoretically)

I have a set of discrete points on a 2D surface and need to build a heat map or a distribution of the density of the points. However, I also need to smooth out the density/distribution by applying ...
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1answer
18 views

Distribution of distances to an observation from the normal and the median of these distances

Given $x\sim \mathcal{N}(\mu=0, \sigma^2=1)$, the squared distances of the $x$ values to $\mu$ are distributed $\chi^2_1$. I am interested in the distribution of the squared distances to an arbitrary ...
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108 views

HPD interval for the mean

Suppose we have iid observation with the following model $ Y_t \sim \mathcal{N}(\mu,1/\mu) , t=1,2,..T$ The question is " Assuming a flat prior on $(0 ,\infty )$ find a 95% HPD interval for $\mu"$ ...
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1answer
43 views

If my normality test is non-significant, am I safe to use the t-test?

I took a 30 unit sample from a population. The sample distribution resulted to be normal. Can I state that the population distribution is normal too? If so, with what level of confidence?
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23 views

Two stage GMM estimator in Matlab

I am trying to create a simple GMM estimator for the mean of a normally distributed random variable using the first three odd central moments of a normal distribution (all of which should be zero ...
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1answer
27 views

2 sampled ks test in r

I need to do a two-sample Kolmogorov-Smirnov (KS) test in R, only I don't understand the formulae and how it works when I look it up. I suspect this is because I ...
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1answer
40 views

Why we check the residuals of ARIMA model for white Gaussian?

I have problem about the assumptions and model verification of ARIMA models. I know that Gaussian distributed assumption is not necessary for fitting ARIMA models but I wonder why a lot of people ...
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1answer
65 views

Best statistical notation for expected probability density

Assume that we have two multivariate normal distributions $\mathcal{N}_1 = \mathcal{N}(\mu_1, \Sigma_1)$ and $\mathcal{N}_2 = \mathcal{N}(\mu_2, \Sigma_2)$. We do these two steps: Pick a point, say ...
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1answer
18 views

How can the density of a truncated normal distribution be greater than one?

According to the info in the following locations: http://en.wikipedia.org/wiki/Truncated_normal_distribution http://en.wikipedia.org/wiki/Truncated_distribution ...
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1answer
29 views

What is the difference between elliptical Gaussian and multivariate Gaussian distributions?

I am reading about Metaelliptical copulas but I don't know the difference between elliptical Gaussian and multivariate Gaussian distributions I would appreciate if somebody can explain the difference ...
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28 views

model noise with Gaussian(0, Gamma)

Can anyone help me in understanding what kind of noise is it? Noise = Normal(0, v) v = GammaFromShapeAndRate(alpha, beta) I mean what is the advantage of making a normal noise with a Gamma ...
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4answers
140 views

Is there a desription in the literature of a Normal hierarchical model with hyperparameters for both the mean and the standard deviation?

I'm looking for a comprehensive description of and justification for a Normal hierarchical model where both the means of the groups and the standard deviation are modelled. It is common to find ...
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1answer
41 views

Normal prior for Binomial likelihood [closed]

Pardon my ignorance, i am new to Bayesian Analysis. I am trying to use Normal prior for a binomial likelihood, which of these are most likely candidates ( $\bar{x} $, $ \mu $, $ \sigma $ ) ...
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75 views

Why not use the T-distribution to estimate the mean when the sample is large?

Basic statistics courses often suggest using a normal distribution to estimate the mean of a population parameter when the sample size n is large (typically over 30 or 50). Student's T-distribution is ...
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1answer
113 views

Comparison between MAD and SD

I am reading Huber's Robust Statistics (2nd). On page 2 and 3 he gave an example. The basic facts are summarized here. Let $(X_n)$ be a sequence of random variables and define two measures of spread ...
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3answers
113 views

What is the PDF of $[(X-a)^2 + (Y-b)^2]^{1/2}$ where $X$ and $Y$ are two non-standard normal random variables?

I have to conduct an experiment getting data from a system. These data are the estimated values, provided by the system, of a true value that we know beforehand. I then compare the estimated values ...
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239 views

What is the maximum likelihood estimate of the covariance of bivariate normal data when mean and variance are known?

Suppose we have a random sample from a bivariate normal distribution which has zeroes as means and ones as variances, so the only unknown parameter is the covariance. What is the MLE of the ...
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3answers
85 views

Cumulative distribution function: what does $t$ in $\int\exp(-t^2)dt$ stand for?

I'm trying to teach myself how to quickly translate many different types of equations into VB, T-SQL and MDX code. Since I'm trying to build a skill, not just solve a single isolated problem, I'm try ...
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31 views

How does Standard Deviation (Error) change with sample size change in this scenario. Explanation needed for a nonprofessional

I have this question that I want figured out. A person's Blood pressure was taken 4 times,the mean of these 4 observations came out to be say 120mm of Hg And the SD was 2.5. Now we have taken 4 more ...
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33 views

Normality test with p-value equal to zero [duplicate]

I have an array dataset of about 650.000 points. I want to test if the dataset follow a normal distribution or any other distribution. The first thing I did was to split the data in groups, find the ...
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2answers
78 views

Does joint normality imply marginal normality?

If it is given that an $N\times1$ random vector ${\bf x} = [x_1,x_2,\ldots,x_N]^T$ has a multivariate normal (MVN) distribution, it implies that all constituent random variables $x_n; n\in[1,N]$ are ...
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1answer
30 views

Does Normal distribution theory originate in the psychometric literature, especially reliability theory?

The basic statistical literature does not talk about the exact background of the normal distribution. Is the basis of this assumption in psychometry or it has an origin in pure statistics i.e. ...
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15 views

Merge two different plots: one in the X-axis and the other in the Y-axis [migrated]

I have the represented independently these two plots using R: PLOT 1 ...
1
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1answer
41 views

Student t-distribution

If $X_i$, $i =1,...,n$ all follow a normal distribution $N(\mu,\sigma^2)$, and are independent, does $\frac{\sqrt{n}\cdot(\frac{1}{n}\cdot \sum X_i - \mu)}{\sqrt{(\frac{1}{n}\cdot \sum (X_i-\mu)^2)}}$ ...
2
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1answer
139 views

Will I go to UC Berkeley?

I forget where I got this data (I think from About.com College), but here are some statistics regarding University of California, Berkeley admissions: the 25th percentile SAT Reasoning Test score was ...
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3answers
52 views

Biased coin toss simulation — which random generator is most appropriate?

I have a doubt whether the uniformly distributed random generator is the most appropriate to use for simulating biased coin toss. ...
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20 views

Rice distribution: estimate $\nu$ from 2D-data

How can I get a good estimate of parameter $\nu$ of the Rice distribution based on a set of $(x,y)$-coordinates? Edit: Given whuber's excellent comment, I'm not looking for an unbiased estimate. ...
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1answer
54 views

Multivariate normal distribution has peaks

I'm trying to calculate a bivariate normal distribution in matlab(with mvnpdf), but the pdf I obtain has a strange shape with several peaks. This is the code I use: ...
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27 views

Mean and variance of a general multivariate skew normal distribution

I have a problem about a general multivariate skew normal distribution. There is a $p\times 1$ vector, $\mathbf{y}=(\mathbf{y}_1',\mathbf{y}_2',\ldots,\mathbf{y}_n')',p>n$, which has the density as ...
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1answer
25 views

Simulating outcome of 3 political parties

First I'm sorry I couldn't figure out the most accurate title for this question (suggestions welcome). Here's the case: I want to implement spinners like the ones on this page: ...
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1answer
26 views

How to justify the statistical independence among two sets of continuous multivariate observations

I have two sets of continuous multivariate observations $X=\{x_1, x_2, ..., x_d\}$ and $Y=\{y_1, y_2, ..., y_d\}$. How can I justify if they are statistically independent or not? For simplicity, I ...
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1answer
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Area under a truncated distribution = 1

I have computed a truncated normal distribution, which total probability density (i.e. area under the curve) is equal to 0.92. The distribution represents well the reality of the phenomenon I am ...
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45 views

Statistic for count process and measurements

I am facing some problems concerning which statistical approach to use for my measurements. I have a sensors which counts how many times an events occured. I had to characterize two lots of sensors, ...
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1answer
27 views

How to model the prior distribution of several Gaussians with known parameters

I might be wrong, I just feel that the following case is different from the problem of modelling observations with a conjugate prior: Suppose I have $n$ different Gaussians each with a different (but ...
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1answer
27 views

How to sample from the distribution of a Gaussian scale parameter

I would like to be able to sample the standard deviation of a multidimensional Gaussian distribution of dimension $n$; that is, given some $\phi$, I would like to sample $P(\sigma | \phi) \propto ...