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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Generating weights with a normal distribution (Mediation analysis)

This mediation analysis regards how much of the social inequality (as a binary exposure) in long term sickness absence is mediated through physical work environment. The mediator is the logarithm of ...
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11 views

Inference about two samples

I have two different large samples, one is normally distributed (0,1) and the other one follows a t-distribution (df = 4). Can I compare whether the means or the st. deviations of both samples are the ...
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1answer
17 views

Formula for confidence interval level doesn't give correct result

I am kind of new in calculation of confidence interval, so I hope it will not be a too basic question. I have a normal distribution (with slightly longer left tail) as you can see in the picture. The ...
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1answer
18 views

What does it mean that a variogram keeps increasing with distance?

I am modeling my 3D dataset with a Gaussian Process with square-exponential covariance. To test whether this is a good model, I subtract the mean from the observed data and then calculate the ...
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1answer
16 views

Effect in linear model versus effect in mixed model

Consider a dataset with 3 observations pertaining to 5 patients. This can be modeled in several ways, two of which are that $$ X_{ij} = \xi_i + Y_j + \epsilon_{ij}, $$ $i = \{1,..,3\}$, $j = ...
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3answers
103 views

Testing for specific normality in R

Is there a command in R, for which I can compare my specific sample to some specific (given) normal distribution? Like a qqnorm testing for the specific normal distribution ...
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1answer
47 views

Can you test for normality for a (0,1) bounded distribution?

I have a vector of observations called MyData which is a percentile score that is >= 0 and <= 1. I would like to test the ...
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1answer
15 views

How do I sketch (on paper) the scatter plot with given covariance matrix and expectation vector?

I have found some information concerning my problem, but I am too unfamiliar with statistics to fully grasp the concepts explained. Also, much of the explanations are written for python/Matlab/R code, ...
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3answers
114 views

What is the distribution of $X_i-\bar{X}$ when $X_i$ has $N(\mu,\sigma)$ distribution

Suppose $X_1,X_2,...,X_n$ be iid random variables with $N(\mu,\sigma^2)$ distribution. We know that $X_i-\mu$ has a $N(0,\sigma^2)$ distribution. My question is what is the distribution for ...
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15 views

Does White noise has a Normal (Gaussian) Distribution? [duplicate]

What I know: White noise process is random process whose power spectral density is constant for all frequencies. ( Sure about this) White noise process has mean zero. (Not sure about this) Gaussian ...
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1answer
22 views

Finding outlier values for non-normally distributed data

I have univariate data (38 is the sample size).The distribution is certainly not normal. How can I find the outliers? I used z-score but am not getting a desired result.
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64 views

How can I have the sigma of a normal distribution when I have f(μ)?

How can I find the standard deviation $\sigma$ of a normal distribution satisfying the following criteria? \begin{align} μ &= 12 \\ f(μ) &= 0.5 \end{align} Basically, I have the mean $μ$ and ...
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1answer
81 views

How to calculate the total probability inside a slice of a bivariate normal distribution in R?

I have a bivariate normal distribution composed of the univariate normal distributions $X_1$ and $X_2$ with $\rho \approx 0.3$. $$ \begin{pmatrix} X_1 \\ X_2 \end{pmatrix} \sim \mathcal{N} \left( ...
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25 views

Joint probability and normal random variables

Say that A and B are independent and continuous random variables, and the normal distribution of A is N~(10,1), B is N~(5,2). Is the normal distribution of A and B jointly simply N~(15,3)? If no, ...
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1answer
47 views

Linear regression with unbalanced dummy variables + not normally distributed residuals

I am conducting a multiple linear regression analysis in SPSS. My DV is a score between 0 and 6, and my predictors are: one dichotomous nominal variable (native vs. non-native speakers) one ...
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ANALYSIS OF COMPARING MEAN OF TWO GROUP (HIGH SCHOOL STUDENTS AND ADVANCE STUDENTS [closed]

ANALYSIS OF THREE INDEPENDENT VARIABLE AS CAUSAL TO DEPENDENT VARIABLE(TITLED determinants of career choice) mentioned three determinants) socioeconomic status,personality and future expectation ...
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12 views

Tail Bound from Asymptotics of an Estimators

Consider an non-parametric estimator for a random variable $X$ is $\hat{X}$. We know an asymptotic convergence for this estimator, in which $N^{1/4}\left(\hat{X} - X ...
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6 views

About the evaluation of covariance of linear Gaussian model in PRML

Section 8.1.4 of Pattern Recognition and Machine Learning introduces the linear Gaussian model where each node has distribution $$ p(x_i \big|pa_i) = \mathcal{N}\left ( x_i \Bigg| \sum_{j\in ...
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24 views

How to draw samples from a multivariate Gaussian distribution without having access to a function that does the job? [duplicate]

I am using the programming language Lua which does not have any built-in function for drawing samples from a multivariate Gaussian distribution. So I wonder, how can one implement a function that does ...
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1answer
39 views

What is probability that one normal random variable is max of three normal random variables?

I have three independent random variables, $X_1$, $X_2$, and $X_3$, and each random variable has different mean. (And I assume they have the same variance). I would like to know how I can get the ...
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25 views

Does the unconditional distribution of $y_i$ only depend on the distribution of the errors?

In linear regression, does the unconditional distribution of $y_i$ only depend on the distribution of the errors? For example, is it not the case that if $$y_i = \beta_0 +\beta_1 x_i + u_i $$ and ...
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17 views

Service Level Caluclation with Double Truncated Normal Distribution

The purpose of this exercise is to determine how the number of employees working affects the service level of their job within the organization they are a part of. EX. A call center gets 100 calls a ...
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14 views

Finding discrepancies in distances between random variable samples

There are $N$ independent and unknown points $p_i$, $q_i \in \mathbb{R}^3$, $i \in [1, N]$. I want to find if the pairwise squared Euclidean distance of each $i$ pair is the same for all of them, or ...
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1answer
15 views

Suggestions for simple model of who wins the league in a game of fantasy football

In a game of fantasy football players score points each week depending on the team they have selected, and at the end of a season the player with the most points wins. There are $W = 38$ weeks, and a ...
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1answer
99 views

The product of two lognormal random variables

Let $X_1$ and $X_2$ be two normal random variables. Write $X_1\sim N(\mu_1, \sigma^2_1)$ and $X_2\sim N(\mu_2, \sigma^2_2)$, to fix ideas. Consider the corresponding log-normal random variables: ...
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1answer
17 views

uniform histograms in copula approach

I would like to model some time series. For this purpose I have the marginal distribution and want to use a gaussian copula to build the dependency. Following a tutorial the following should give me ...
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48 views

Does the product of three Gaussian random matrices converge in distribution to a Gaussian?

Suppose we have vectors $u,v \in \mathbb{R}^r$ with and matrix $W \in \mathbb{R}^{r \times r}$ where all entries of $u,v,W$ are iid $N(0,1)$. Does the following hold? \begin{equation} \frac{1}{r} ...
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2answers
43 views

How does Gibbs sampling produce values for a variable using the univariate conditional probability?

I have a question about Gibbs sampling for generating samples. The Gibbs sampling algorithm is often stated. $x^0 = (x_1^0, x_2^0, \ldots, x_n^0)$ //initialize random values for $t=1$ in $T$ ...
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50 views

Variance of a Cumulative Distribution Function of Normal Distribution

Suppose, $X\sim N(\mu,\sigma^2)$. Can anyone help in finding the following : $\text{Var } \bigg(\Phi\big(\frac{X + c}{d}\big) \bigg)$ ? Here, c and d are positive. Here, $\Phi(x)$ is the ...
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2answers
599 views

What is the name for the distribution shape of a histogram with this kind of curvature?

I have a histogram of points with a dip in the center of the bell, seeming to create two bells, or two clusters. What is the name for this kind of shaped distribution? This curve should be normal but ...
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2answers
69 views

What to do with data that are bimodal at two tails of the distribution?

I am in a weird position where I prespecified a plan to use linear regression to analyze my data, and stated I would use transformations to address any assumption violations. I'm pretty certain my ...
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1answer
17 views

Evaluate high-dimensional Gaussian with variance matrix $\sigma^{2}I_{n_{t}\times n_{t}}+\boldsymbol{\Sigma}_{t}\boldsymbol{\Sigma}_{t}^{'}$

I need to compute the log-likelihood function in a high-dimensional Gaussian time-series. I have the following model: ...
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1answer
50 views

Use z-scores to determine the best strategy for airlines

Most airlines board passengers starting from the back of the plane and then working their way towards the front (after boarding priority classes and passengers). In an episode of Mythbusters, Adam ...
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1answer
28 views

From interaction model to additive model

I have two factors, and I've fitted a interaction model in R with $lm( \sim factor1*factor2)$. The parameters belonging to the interactions between the two factors are all non-significant (p-values ...
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1answer
29 views

Normalize non-normal distribution?

I have a query regarding a comment I found, which will surely shed some light. In this article: http://www.analyticsvidhya.com/blog/2015/09/naive-bayes-explained/ I found: If continuous features ...
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7 views

Differences between ML and kernel Gaussian classification strategies

The Gaussian distribution can be used in "parametric" and "nonparametric" classification for new test points. One way to do parametric classification using a Gaussians is to estimate ...
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1answer
36 views

Decomposing a locally stationary covariance matrix

Say I have a non-stationary Gaussian Process with a square exponential covariance whose shape varies throughout space. The covariance entries are: $$ K_{ij} = N(|x_i-x_j|,\sigma_i^2+\sigma_j^2) $$ ...
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1answer
36 views

If my data follows a normal distribution, does that mean my residual are normally distributed as well?

I have a data set which approximately follows a normal distribution. Does that necessarily mean that the residuals (as define) here) of my dataset do follow a normal distribution?
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Variance assumption in normal linear model

How do we test the assumption of equal variance in a normal linear model? The normal assumption is tested by QQ-plot, the independence assumption is tested by the design of the experiment or of how ...
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17 views

What is the analog of WSSSE in Gaussian mixture models?

What is the Equivalent of WSSSE (within set sum of square errors) in K-means in GMM (Gaussian mixture models) using the Expectation Maximization algorithm? In detail: if WSSSE is plotted against ...
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1answer
34 views

Probability of mutually exclusive distributions

The following graph shows at what index number between 0 and 100 the underlying price is followed by a move up, down or whether there's no change. My question is as follows: How does one calculate ...
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18 views

Expectation of “mixed-variables” obtained from a N(0,1) variable

I have a variable $z$ which is normally distributed with zero mean and unit variance. I should derive $$ E[z^+]$$ $$ E[z^-]$$ $$E[z^+z^+]$$ $$E[z^-z^-]$$ $$E[z^+z^-]$$ where $z^+ =max(z, 0)$ and $z^- ...
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1answer
17 views

Increase sample size via algorithm [closed]

If I have a normally distributed dataset with a sample size of 100, what algorithms/procedures can I implement to increase the sample size to 1000?
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11 views

Stationarity of the TGARCH

I'm going through "GARCH models" by Francq and Zakoian (2010). They define the TGARCH(1,1) as $$\sigma_t = \omega + \beta_1 \sigma_{t-1} + \alpha_{1,+}\epsilon_{t-1}^+ - \alpha_{1,-}\epsilon_{t-1}^- ...
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1answer
8 views

How to distinguish real price series from simulated series

Given a set of prices, I want to filter out series which are simulated from normal distribution from real prices observed in market. Is there a determining factor between real and simulated price ...
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1answer
57 views

Measuring how well a new vote fits to a model of existing votes

My knowledge in statistics is very limited, so I hope this is actually an easy question. I am working on a kind of survey application where users either vote between a finite number of discrete ...
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2answers
71 views

What's in a name: Precision (inverse of variance)

Intuitively, the mean is just the average of observations. The variance is how much these observations vary from the mean. I would like to know why the inverse of the variance is known as the ...
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22 views

Why is the standard deviation the error on the singular measurement?

I'm a beginner with the study in data analysis in Physics. I'm trying to understand the meaning, in the field of experimental Physics, of the standard deviation $\sigma$ of a series of data. There ...
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14 views

How to run 2 Way ANOVA on SPSS with data that is not normal distributed?

I am about to run 2x2 ANOVA on my data, but then I realized that my data is not normal. I have tried to do data transformation like Log10 and Ln, but the data is still not normal. The data has ...
4
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1answer
114 views

Gaussian with a Gaussian mean

Sorry if the question is ill-phrased, but I'm pretty new to this and I have the following situation: I know that samples X is drawn from a Gaussian Distribution G(u, v). Now that if u is substituted ...