# Tagged Questions

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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### What interesting things can be said about the distribution of the range of a sample from a normal population? [on hold]

http://math.stackexchange.com/questions/1874363/how-to-find-range-when-mean-and-standard-deviation-is-given-in-a-normal-distribu This $\uparrow$ question inspired me to do a small simulation: ...
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### supervised binning of features [on hold]

Trying to understand the statistical technique that can be used to solve this problem- I have set of independent features (x1,x2,x3,x4,x5) both continuous and discrete. The dependent variable is ...
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### How to test differences in means in a population that is not normally distributed, heteroskedastic and differs in variance?

I want to test if the means of two populations are different from each other. There are 12 poulations, all with different sample size, ranging from 48.000 to 300. Here is a 20.000 rows sample. The ...
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### QDA vs EM with Gaussian likelihoods

QDA (quadratic discriminant analysis) assumes that the K different classes are generated by K different multivariate Gaussians, each with potentially different mean vector and covariance matrix. If ...
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### does census data has to follow a normal law before doing a mean comparison by an ANOVA?

I'm working on some socio demographical (Age, tenure, salary, etc...) data to predict absenteism. I have all the employee data, so i have the entire population. When i run a descriptive analysis for ...
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### Can the 68-95-99.7 rule be used to test normality?

Suppose I have a data which has 90% values in $\pm 1 \sigma$ range, 98.8% values in $\pm 2 \sigma$ range and 99.9% values in the $\pm 3 \sigma$ range. Can I refute that this data is distributed ...
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### p-value for non normalized data [on hold]

I'm working on a project where I want to apply the output of a neural network in conjunction with a greedy (prediction) algorithm. The project is segmentation of 3D volumes. The greedy algorithm ...
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### How can I test normality of data incrementally?

I plan to track the mean and variance of a data set as it grows over time, but I can't keep the actual data, just the current mean and variance. Later, I want to estimate the probability of a given ...
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### how to preprocess/feature stacle multimodal input data?

I am wondering how to normalize data for the use of SVMs etc. that has a clear non Gaussian, i.e. non unimodal distribution. I wrongfully scaled the data by subtracting the mean and dividing the std ...
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### Finding lower proportion limit of a sample distribution

Problem description If a population proportion is 0.28, and if the sample size is 140, 30% of the time the sample proportion will be less than what value if you are taking random samples? This ...
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### multivariate normal distribution. And marginals distributions [duplicate]

if $X_1$ and $X_2$ are random variables that marginally have a normal distribution, is it true that the joint $(X_1,X_2)$ has a distribution according to a multivariate normal density distribution? ...
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### Should I remove the outlier?

I want to run an ANOVA test. I am therefore testing for normality. I have tested each group and the residuals (group together)for normality. My data sample does not look approximately normal. However ...
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### Is this close enough to be normally distributed for using a parametric test?

Can I say that the values are close enough to be normally distributed? The histogram does not look normally distributed at all, but the Q-Q plot is not so far away. My sample size is 30. The shapiro-...
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### Estimating the Parameters of Multivariate Gaussian from Conditioned Distributions

My goal is estimating the distribution parameters of a multivariate Gaussian $\mathcal{N}(\mu,\Sigma)$ in $\mathbb{R}^n$ from observations that were generated from different conditioned variants of ...
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### Is there any type of distribution which has zero-mean, unit-variance; but, is non-Gaussian?

The standard normal (Gaussian) distribution has zero-mean and unit-variance. I wonder whether there is a zero-mean, unit-variance, and non-normal (non-Gaussian) distribution or not?
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### Independence of random variables with known Gaussian conditional distributions

My question regards whether it's possible to know whether two Gaussian random variables are independent when we know only that their respective laws are governed by conditional distributions of ...
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### why does this election vote converge to bell curve?

Law of large numbers central limit theorem says IID random variables deviate from their average like a Gaussian, but these state matchups have different outcomes and probabilities. In fact, they are ...
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### Should standardization be done using leave-one-out?

When we have data from a normal distribution, we may wish to standardize the values in our sample to $N(0,1)$. In such case it is customary to divide each observation by the sample mean and standard ...
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### PyMC sampling is slow

I'm using pymc2 to estimate the parameters of a normal distribution. My data has shape 50000 x 6. Basically, I have 50K independent distributions and I want to obtain the parameters for each of them, ...
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### Finding probability assuming null hypothesis is true

Candidates 1,2 and 3 are running for a position in a company. Candidate 1 claims 38% favourability among all the voters. Assuming this is true, what is the probability that in a random sample of 500 ...
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### Test for normality with outliers produces strange p-values

I try to create some example that show how an outlier causes non-normality. Therefore I created two datasets: A dataset with normal distributed data ...
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### Why are points uniformly distributed on a sphere in 3D uniformly distributed in component coordinates?

I've generated uniformly random points on a sphere (in 3D). As expected, all azimuthal angles are drawn with equal probability and it's less likely to draw points close to the poles: However, when ...
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### Appropriate data transformation

I have two dependent variables y1 and y2 with highly skewed distributions. In order to do ANOVA, I was trying to transform the ...
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### How do I calculate (or approximate) the covariance matrix of a multivariate Gaussian distribution with only the variances of the components?

With the constraint that all components sum to a given specific real number; The Mean vector is also known; No sample available; correlations between any two of the components is unknown.