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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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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40 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
32 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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19 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
23 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
39 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 ...
2
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1answer
64 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
28 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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27 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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2answers
67 views
+50

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
38 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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3answers
72 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
112 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
111 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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2answers
233 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
82 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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30 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
74 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
26 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 ...
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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 $\frac{\sqrt{n}\cdot(\frac{1}{n}\cdot \sum X_i - \mu)}{\sqrt{(\frac{1}{n}\cdot \sum (X_i-\mu)^2)}}$ ...
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1answer
138 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
46 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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22 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
24 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
11 views

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
26 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
26 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 ...
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18 views

Distribution of sum of squared normal distributions with different means and variances? [duplicate]

Let $ Z=X_1^2+X_2^2\cdots\cdots X_j^2 $, such that $X_i \sim \mathcal{N}(\mu_i,\sigma_i^2)$. All $X_i$'s are independent of each other and $\mu_i$ and $\sigma_i^2$ are all different from one another. ...
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420 views

Why does the t-distribution become more normal as sample size increases?

As per Wikipedia, I understand that the t-distribution is the sampling distribution of the t-value when the samples are iid observations from a normally distributed population. However, I don't ...
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24 views

Low pass filter to maintain edge information

I am looking for a kernel as low pass filter that satisfy as:I must find a kernel that statisfies as follows: In the my reference paper, the author suggest gaussian kernel that is The gaussian ...
2
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2answers
287 views

How to transform a normal random variable such that I can simulate normal samples between the range of 1 and 45?

How to transform a normal random variable such that I can simulate normal samples between the range of 1 and 45? Do I need to do a jacobian transformation ?
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1answer
61 views

Normal distribution to triangular distribution

I would like to know if it is possible to convert a normal distribution into a triangular distribution. If it is, how it can be done? I know the mean and the coefficient of variation of the normal ...
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2answers
44 views

Plotting a Gaussian in Python

I am trying to plot a histogram of my data, and I seem to be a little confused here. I am using matplotlib in Python. Here is the code from their website: ...
3
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1answer
65 views

Infinite fourth moment and maximum entropy

Alright, I expect this is a silly question, but I don't actually know, so. Suppose there is some random variable that's distributed on the reals, and all I know about the distribution is its mean ...
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1answer
266 views

Which is kernel similar gaussian kernel?

I must find a kernel that statisfies as follows: In the my reference paper, the author suggest gaussian kernel that is The purpose of that kernel is that it will take a weight for each points ...
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90 views

$E(\frac{1}{1+x^2})$ under a Gaussian

This question is leading on from the following question. http://math.stackexchange.com/questions/360275/e1-1x2-under-a-normal-distribution Basically what is the $E\left(\frac{1}{1+x^2}\right)$ under ...
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1answer
29 views

Analyzing regression results

I have done a regression model where i determine the number of cubes (independent variable) based on the amount of units i started with for each product type (dependent variables, ...
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2answers
99 views

Proving some properties of expected first order statistics with respect to sample size

Question: Consider $n$ random variables $x_1, x_2,\cdots x_n\sim \mathcal{N}(0,1)$. The expected value of the $i$th order statistic (the maximum) can be written as $E(\mathcal{O}^n_1)= ...
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Normal Bayesian Model: Marginal distribution of $\bar X$ with unknown mean and unknown variance

For $i=1, \ldots, K$ and $j=1, \ldots,n$, assume the following model. \begin{align} X_{ij} \mid \mu_i, \sigma^2 & \stackrel{_\text{ind}}{\sim} N(\mu_i, \sigma_i^2) \\ \mu_i & ...
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When doing ANOVA, what do we need to assume is normally distributed? [duplicate]

Do we assume that the population distributions are normal, or that the sample distributions are normal, or that the sampling distribution is normal? If the latter, what do we mean by sampling ...
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1answer
75 views

Is it Poisson distributed, and if so, what's its meaning?

I've collected data from my website. The website is about cars. The data are about user reviews and the cars. what we see in the graphs is the probability of some car type (Ford Focus 2008) to have X ...
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2answers
28 views

Evaluate mixture model

I have a question concerning the evaluation of mixture models. Is there a gold standard to compute the goodness of a fit for a mixture model? What I am concerned about is how one would evaluate if ...
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1answer
89 views

The standard normal distribution vs the t-distribution

Given an IID normally distributed sample $X_1,...,X_n$ for $n$ small with mean $\mu$, standard deviation $\sigma$, sample mean $\overline{X}$ and sample standard deviation $s$ (the unbiased estimator ...