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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Analyzing the effect of categorical variables on a correlation coefficient

For my research project, I’m looking for some help on how to analyze my data. The research setup is as follows: I’ve got two normal variables that I want to correlate with each other and a number of ...
3
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2answers
105 views

Sampling from a product of two Multivariate Gaussians

I have a multivariate Gaussian defined as follows: $$ p(x) = \omega(x)\gamma(x) $$ where $\omega$ and $\gamma$ both are multivariate Gaussians and from which I can sample very efficiently given due to ...
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1answer
22 views

Percentage with Normal Distribution

Based on the picture below, there is a value with a percentage that is 68 and 95 percent in relation to standard deviations in a normal distribution. My question is: What do the 68 and 95 percentages ...
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0answers
9 views

Fitting data in multivariate Gaussian

I have a dataset of N*d feature vectors and I was asked to fit them in a multivariate gaussian, with a matlab function (that someone else has programed) that recieves the number of points, mean and ...
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2answers
30 views

Normality test for repeated measures data

I've measured the motor function of the same subjects (n=6) over 7 different time points. I would like to know whether the mean motor function varies significantly with time (day 1 versus day 2 etc) ...
2
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1answer
59 views

How to calculate variance of Gaussian given mean and average deviation

I want to calculate the variance sigma of a Gaussian (normal) distribution given its mean mu and average deviation d (i.e. average of absolute value of difference from the mean). How can I do this? ...
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0answers
8 views

Kernels determination in Gaussian Regression multiple input features

How can i choose a proper kernel for Gaussian Regression when i have more than one feature in my inputs? I am relatively new to this and all the lectures and most literature seem to have described ...
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2answers
68 views

Predictive posterior distribution with multivariate normal distribution

Suppose I have a multivariate normal ${\bf{Y}}|{\bf{\theta}} \sim {\bf{MVN}}(X {\bf{\beta}}, \sigma^{2}H(\phi))$ where ${\bf{Y}}$ is a set of observations ${\bf{Y}} = ...
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0answers
20 views

How to model the sampling distribution of the sample sum

I'm stuck on a stats problem and am wondering if someone can point out the error in my logic. Imagine you are planning for a camping trip for 50 people. Each person consumes 2.0 lb of food per day on ...
2
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1answer
34 views

Overlapping Coefficient between for two Gaussian distributions where one of them has zero variance

Consider the case where we have two Gaussian distributions and we are trying to find the area of overlap between them. This is also called the Overlapping Coefficient and I think it is also related to ...
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1answer
32 views

R: random sampling for multivariate normal and log-normal distributions

I want to generate random monthly (m) temperature (T) and Precipitation (P) data considering that both variables are intercorrelated (rTP[m]) The tricky thing is that my random variables that have ...
32
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9answers
4k views

When teaching statistics, use “normal” or “Gaussian”?

I use mostly "Gaussian distribution" in my book, but someone just suggested I switch to "normal distribution". Any consensus on which term to use for beginners? Of course the two terms are synonyms, ...
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63 views

conditional expectations

Hi i was wondering how to figure out the following Suppose $y=x+e$ where e is an i.i.d error. Say $x \sim N(\mu,\sigma_1^2)$ and $e \sim N (0, \sigma_e^2)$ which means $y \sim N (\mu, ...
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0answers
38 views

Estimate multivariate distribution of dependent variables

Let $H$~$\mathcal{N}(\mu_H,{\sigma_H}^2)$ and $S$~$\mathcal{N}(\mu_S,{\sigma_S}^2)$. $H$ and $S$ are dependent of each other and their covariances are unknown. Let $G = H - S$ and the mean and ...
2
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1answer
54 views

First order statistics (min) of n non-identical but independent normal variates [duplicate]

While I have seen papers and posts about mean and variance of n i.i.d normal random variables, I am looking for the first order statistics of $n$ (specifically $11$) normal, non-identical (different ...
0
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0answers
29 views

Maximizing pH values based on mean

It is required to maintain the pH of the water at 7.5 plus or minus .5 in a water treatment process. Two methods of treatment are available. Method 1 gives a mean pH of 7.5 and standard deviation 1.0, ...
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0answers
35 views

Probability that one person's weight is more than 50 pounds greater than another's

The weight of a Portuguese man is normally distributed with mean 160 pounds and standard deviation 30 pounds. The weight of a Portuguese woman is normally distributed with mean 120 pounds and ...
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2answers
31 views

Would it be incorrect to apply tests appropriate for normal distribution to data with the following distribution?

Histogram showing the frequency for test scores (range 15-75) for a total of 91 students.
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1answer
60 views

Using chi goodness of fit to test if data comes from normal distribution

The problem gives 50 observations and then asks to check whether the data comes from a normal distribution. For instance if these are your observations then how would you go about testing to see if ...
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0answers
47 views

Transform long tail data set to bell curve [closed]

I'm analyzing a data set that has an extremely long tail, and I'm looking for a way to transfer the data into a bell curve so I can apply statistical analysis to it. Hope this makes sense, any help ...
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24 views

Not normally distributed dependent variable in moderator analysis

I have been running a multiple moderator analysis in a pretty simple model. X are Google search queries normalized to 0-100. Y are the new registrations of cars in one country and one moderator. ...
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1answer
35 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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0answers
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
47 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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0answers
20 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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3answers
108 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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29 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
52 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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35 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 ...
3
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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 ...
0
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2answers
52 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
64 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 ...
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1answer
230 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
89 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
27 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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114 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 $\mu"$ ...
2
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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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1answer
43 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 ...
1
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1answer
33 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 ...
0
votes
1answer
46 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
votes
1answer
69 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 ...
0
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1answer
19 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
30 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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0answers
31 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 ...
2
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4answers
143 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 ...
0
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1answer
46 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
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 ...
6
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1answer
116 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 ...