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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4 views

Check for normality: Is it possible to combine variables to get an overall view?

I am trying to do a normality test in order to check whether I can calculate the pearson correlation afterwards. I have read a lot about the three ways to check for normality and generaly found the ...
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1answer
47 views

About simple linear regression

If we assume a vector $y$ which has normal distribution with mean m and covariance matrix M. A simple linear regression model ...
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26 views

When is non-normality severe enough to warrant using different tests?

I've been doing quite a bit of reading on the topic of non-normality, and how it pertains to the F-test. My understanding is that non-normality tests aren't very useful, as outlined in the arguments ...
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20 views

How to generate data for gaussian distributions in these 2 scenarios in R? [migrated]

In "Elements of Statistical Learning" by Tibshirani, when comparing least squares/linear models and knn these 2 scenarios are stated: Scenario 1: The training data in each class were generated ...
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30 views

Is my work acceptable? (Fitting a normal distribution) [on hold]

Sorry for the long text. But please note that what I'm asking for is not a word by word correction, but I'm asking you to do a quick skim (or two) on my method of working, and I hope to get some ...
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16 views

Adjusting standard deviation for 90% acceptance in normal distribution

A Company produces pins. Average length, μ = 1.008 Standard deviation, σ = 0.0045 Sample size, n= 50 Sample is bought by customer only if it is within interval 0.99 to 1.01 inch. If only ...
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2answers
11 views

What do the remaining columns (after column 2) in a Z table mean

In the Z table , I can understand the first 2 columns. The first column is the Z value, the second column is Prob(X<=Z). But what do the remaining columns mean?
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9 views

Analyzing time to event variable that has an upper limit cutoff

Setup: 4 different interventions, outcome metric: time for subject to respond. So lets say that for three of the groups of subjects they responded within 5 to 20 seconds. However, in one group, the ...
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2answers
94 views

Inference on $P\left(\left.\sum_{i=1}^{N}X_{i}\ \right|\ \sum_{i=1}^{N}X_{i}^{2}\right)$ when $X_{i}\sim\mathcal{N}\left(0,1\right)$?

Let: $$X_{i}\overset{i.i.d}{\sim}\mathcal{N}\left(0,1\right)$$ Hence: $$\sum_{i=1}^{N}X_{i}\sim\mathcal{N}\left(0,N\right)$$ and $$\sum_{i=1}^{N}X_{i}^{2}\sim\chi^{2}\left(N\right)$$ What can ...
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30 views

Under what circumstances will the log of a variable be normal, given that the variable is not normal

Let us say there is a variable that is not normally distributed. Under what circumstances will the natural logarithm of the variable be normally distributed? I have seen many articles and papers ...
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10 views

Axes having different scales on a q q plot

I was trying to learn linear regression in SAS using this example When I came to the part about the q-q plot: ...
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12 views

Comparing normalized and partially normalized quadratic form of normal variables

Suppose $X=(X_1,X_2,\ldots,X_n)' \sim \mathcal{N}(0,\Omega)$, where $\Omega$ is the variance-covariance matrix of dimension $n\times n$ for the vector $X$. Let $a=X'\Omega^{-1}X$. It is known that ...
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5 views

Objective evaluation of subjective data points and normalization

I want to write an access database that takes in inputs from instructors ranking a student on their performance in a handful of categories. (1 - below average, 2 - average, 3 - above average). They ...
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0answers
15 views

Efficient computation of a (truncated) distribution's parameters given the moments (and back)

I have a probability distribution of the form: $$p(\vec x) = Z^{-1} \delta\left(\sum_i x_i\right)\exp \left[ \sum_i (\phi_i x_i + \psi_i x_i^2) \right]$$ for $\vec a \le \vec x \le \vec b$, and ...
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0answers
17 views

Applying parametric tests on non-parametric data

I'm doing a research and I have some concerns, and I'd appreciate your kind assistance on them. Basically, I'm designing an instrument to measure something (a single dependent variable), and I'm ...
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0answers
16 views

Combining two conditional probability distributions; what is the variance?

Say I have two conditional probability distributions: ($Y_1$ | $Z_1$,$Z_2$) ~ N ($\dfrac{a_1B_2Z_2}{1-a_1a_2}$ , $\dfrac{a_1^2+1}{(1-a_1a_2)^2}$)    and ($Y_2$ | $Z_1$,$Z_2$) ~ N ...
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2answers
32 views

How close does a distribution have to be to normal, in order for predictions to be accurate?

I know a Kolmogorov-Smirnov test will tell me if a sample distribution belongs to a normal distribution or not, with a certain probability (correct me if I am wrong?). I performed a KS test on my ...
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57 views

Log-likelihood proof and AIC hypothesis

First of all, statistics is just not my thing ... yet (I hope!) I'm having a hard time finding out the log-likelihood equation: Given $Y \rightarrow \mathcal{N}(\mu_1,\sigma_1)$ (observation) and ...
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1answer
56 views

Multi Armed Bandit for Continuous Rewards - Extended Question

This question is an extension to A continuous generalization of the binary bandit The Multi-Armed Bandit (MAB) Problem in general is described here: https://en.wikipedia.org/wiki/Multi-armed_bandit ...
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1answer
45 views

constant $times$ distribution

I know that if $U\sim\chi^2(k)$ then $aU\sim \Gamma(k/2,2a)$ for $a>0$. But i read about the estimator and its distribution $$\hat{\sigma}_k^2=\frac{1}{2k}\sum_{i=1}^k ...
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1answer
37 views

Generate random number with normal distribution?

I encountered this question, where given it is a normal distribution, how do we go about it to generate a series of random numbers beside Monte Carlo? The clue given was using exponential function.
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1answer
37 views

Covariance Matrix with all equal entries

by training a Gaussian Process Regression Model I'm finding the weird result where the resulting covariance matrix has all the entries equal between each others. I'm using a Gaussian kernel with ...
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1answer
31 views

Can we calculate Z-score for any distribution?

Is z-score only confined to normal distribution or can it be used for any distribution
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9 views

Comparing z scores to Binary data

I have a set of quantitative data for which i have calculated the z scores. I also have a set of qualitative data in which parameters have been assigned scores of 0 or 1 based on expert opinion My ...
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2answers
35 views

How to estimate 100% confidence interval aka. what is the Z value of standard normal distribution at probability of 100%?

Thinking of the various tests and parameter estimates we perform with 99% confindence interval based on assumption of "normal distribution of errors" I asked myself a question what would be the 100% ...
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56 views

Test for difference in proportions with small probabilities

I want to perform a test for differences between 2 binomial populations. The probabilities are small (usually less than 10 %). I can define the successes as "rare events". I think that the z-test ...
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0answers
52 views

Distribution of geometric mean of normally distributed independent random variables [closed]

Suppose we have $X(i)$ for $i=1,...,n$ normally distributed independent random variables with the same known $\mu$ and $\sigma$ for all: $$X(i) \tilde{} N(\mu,\sigma)$$ Suppose that we take the ...
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34 views

PDF of multivariable function from known distribution of components [duplicate]

How can I determine the pdf of the following function: $$z(x,y) = \sqrt{ax^2 + by^2}$$ given the constants $a,b$, the means $\mu_{x},\mu_{y}$ and variances $\sigma^2_{x},\sigma^2_{y}$ of the ...
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1answer
49 views

Deegrees of freedom of Student's distribution

I'm trying to figure out the distribution of this statistic: $$S=\frac{\frac{\overline{X}-\mu_0}{\sigma / \sqrt{n}}}{\sqrt{\hat{\sigma}^2/\sigma^2}}$$ Where: $\overline{X}=\frac{1}{n} \sum_{i=1}^n ...
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0answers
16 views

Conjecturing asymptotic normality for a sum of dependent random variables

I am hunting for the asymptotic distribution of a scaled partial sum of pair-wise equi-correlated, identically distributed continuous random variables $$W =n^{-\delta}\sum_{i=1}^nY_i(n),\;\; ...
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48 views

How to invert a sparse covariance matrix for spatial data on a grid?

Say we have some gaussian random variables that can be indexed on a grid. A convolution was applied to this grid, so now there is covariance between the grid points. The covariance is given by (see ...
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2answers
271 views

Which probability distribution fits my data?

I have generated a dataset (available here) for which I try to find out the best fitting probability distribution. I first generated uniformly distributed random directions and then calculated the ...
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0answers
10 views

Truncated/censored AR1 normal likelihood

I have a model for some data that I am analysing which is of the form: $W^*_t = \rho W^*_{t-1} + \epsilon_t$ Where $\epsilon_t\sim N(0,\sigma^2)$. $W^*_t$ is a latent (hidden) process, which ...
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0answers
16 views

Sending a variable through multiple distributions

Say you have 5 people and 100 lbs of food. Person 1 (P1) gets to the food first, takes some food, and passes it to P2. P2 takes some of the food and passes it to P3, and on to P4. P5 gets whatever is ...
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2answers
82 views

Expected magnitude of a vector from a multivariate normal

What is the expected magnitude, i.e. euclidean distance from the origin, of a vector drawn from a p-dimensional spherical normal $\mathcal{N}_p(\mu,\Sigma)$ with $\mu=\vec{0}$ and $\Sigma=\sigma^2 I$, ...
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0answers
48 views

How to estimate mean and variance of censored normal?

Supposing I have data which I know is normally distributed, but because the recording process is right censored, how do I estimate the parameters of the distribution?
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5answers
301 views

Standardizing a Standard normal Variable

If I standardize a standard normal random variate , will it be still standard normal ? That is, if $X\sim N(0,1)$ , then can I do $$X^*=\frac{x-\bar x}{sd(x)}$$ ? and will $X^*\sim N(0,1)$ ? In ...
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1answer
20 views

How does normalizing the response affect likelihood?

I have a vector of experiment outcomes, $Q$, and I assume that $Q_i$ are generated by a Gaussian distribution, i.i.d., such that the likelihood is the standard $$\mathcal{L}(q_1, ..., q_n) = ...
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0answers
11 views

MANOVA: What to do with a u-shaped DV?

I am hoping to get some advice on my analysis for my MSc dissertation. I will try to keep it short but please let me know if there is more information I can provide to make the situation clearer. ...
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1answer
30 views

How to efficiently simulate values from a multivariate normal given one of the components?

Suppose $X, Y_i$ for $i=1...n$ are standard normal variable but are also correlated so collectively they come from a multivariate normal distribution. Now the complication is what if I want to ...
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17 views

Common methods for transforming non-normal variable to close to normality

I have a list of time series which contain negative values. Right now I am transforming the time series to all positive values >0 and using the Box-Cox transformation to reduce non-normality. My ...
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26 views

Conditional expectation of error based on multivariate normal variables

I have the following situation; I know the "true" model behind my regression but I am intentionally omitting some variables/regressors to simplify the problem. Suppose the true model is: ...
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0answers
14 views

Confindence of test estimation for gaussian mixture model

A simple Gaussian Mixture approach: I have a learning data $ { (x_1,y_1),(x_2,y_2),...,(x_n,y_n) } $. For learning it, I use a Mixture of Gaussian model and after learning it, I estimate new data ...
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1answer
91 views

Test if two normally distributed random variables have the same mean

We have two independent random variables which follow normal distributions $X_1\sim \mathcal N(\mu_1,\sigma_1)$, $X_2\sim \mathcal N(\mu_2,\sigma_2)$. From the context, we have that $\mu_1\leq\mu_2$. ...
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2answers
95 views

Expected value of x in a normal distribution, GIVEN that it is below a certain value

Just wondering if it is possible to find the Expected value of x if it is normally distributed, given that is below a certain value (for example, below the mean value). Thanks,
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1answer
53 views

Normal distribution and independence

I was reading about white noise and it stated: Although $\varepsilon_t$ & $y_t$ are serially uncorrelated, they are not necessarily serially independent, because they are not necessarily ...
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1answer
66 views

How are percentiles distributed?

I was taking a look at this page, and I can't seem to understand why the frequency plot of the percentiles is uniformly distributed. Distances between percentiles are not equal, so why is the ...
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2answers
61 views

How can I compute $\int F(x \mid a,b)f(x \mid w,z) {}dx$ in closed form?

Suppose $F$ is the cumulative distribution function of the normal distribution with mean $a$ and standard deviation $b$, and suppose $f$ is the probability density function of the normal distribution ...
2
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0answers
26 views

Alternative to ANOVA (beginner)

I have run 15 experiments to compare the effect of different hormone combinations on the maturation on Xenopus oocytes (immature eggs). I am hoping to find the best performing variable. I have 4 ...
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1answer
23 views

What is the covariance when you know the covariance w.r.t. a common variable?

Say you know that ${\rm var}\Bigg( \begin{bmatrix} {\bf x}_1 \\ {\bf x}_2 \end{bmatrix}\Bigg) = {\bf \Sigma} = \begin{bmatrix} {\bf \Sigma}_{11} & {\bf \Sigma}_{12}\\ {\bf \Sigma}_{21} & ...