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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16 views

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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16 views

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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13 views

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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13 views

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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1answer
49 views

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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0answers
11 views

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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1answer
22 views

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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40 views

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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2answers
7 views

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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0answers
17 views

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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2answers
53 views

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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2answers
73 views

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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0answers
21 views

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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1answer
43 views

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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1answer
33 views

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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0answers
18 views

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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20 views

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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1answer
26 views

Proportionality of Mahalanobis distance for Gaussian PDF

According to my notes a Gaussian PDF $f_x(x)$ with $x$ ~ $\mathcal{N}(\mu,C_X)$ is proportional to the following: $$ f_x(x) \propto exp\left(-\frac{1}{2}(x - m_x)^TC^{-1}_x(x-m_x) \right) $$ $$ \...
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17 views

Plotting two normal distributions with overlap [closed]

I'm trying to plot two normal distribution curves into one graph to show the overlap between them. My scenario is simple angle data from the heads of multiple fish split between males and females. ...
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0answers
13 views

Original variograms not honoured after sequential Gaussian simulation

I'm working on sequential Gaussian simulations for geospatial data (using SGeMS). The dataset does not have an normal distribution, so I use the software to normal transform it, then check the omni-...
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0answers
55 views

Inverse of Normal Loss function in Excel [closed]

I am looking for a way in Excel to obtain k by inverting the standard-normal loss function G(k). The CDF and loss function for a a variable z that is normally distributed are defined as The formula ...
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26 views

How to find the Inverse CDF of a Skewed Normal Distribution

The Wikipedia article on the distribution also doesn't seem to specify any formulae on right hand side. Also wolframalpha says there is no closed form solution.
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2answers
144 views

Does a confidence interval carry some extra error for non perfectly normal distributions?

I'm not trying to nitpick but I always want to make sure with stats that I clearly understand the delimitation between exact/theoretical measurements and "real life" measurements. Let's say for ...
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1answer
77 views

Calculating probability of an event involving two normally distributed random variables

I have two normally distributed, independent random variables $S^{(1)}$ and $S^{(2)}$: $$S^{(1)} \sim \mathcal{N}(\mu_1, \sigma_1^2),\ S^{(2)} \sim \mathcal{N}(\mu_2, \sigma_2^2)$$ Given two positive ...
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122 views

How can we get a normal distribution as $n \to \infty$ if the range of values of our random variable is bounded?

Let's say we have a random variable with a range of values bounded by $a$ and $b$, where $a$ is the minimum value and $b$ the maximum value. I was told that as $n \to \infty$, where $n$ is our sample ...
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1answer
50 views

Drawing sample size 1 from a uniform distribution - Difficulty in understanding Central Limit Theorem?

Let's say we have a uniform distribution and we are drawing samples of size 1 so that the mean is the drawn number itself. If we perform this activity sufficiently large number of times we would get ...
3
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27 views

Conditional expectation of bivariate normal

I have been reading Heckman (1979) and have tried to prove some result used (the paper points to a book which does not show the work either). I alter the notation a bit for clarity. Assume we have: $$\...
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0answers
7 views

Variance of nonlinear bearings only model

Consider a state space model for the bearings only observation model. The state vector at time $t$ is ${\bf x}_{t}=(x,x^{.},y,y^{.})^{\top}$. The state transition model is ${\bf x}_{t}=F {\bf x}_{t-...
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11 views

Accuracy of sampling from a Gaussian distribution

I am currently sampling data points out of a Gaussian distribution with a particular mean and standard deviation. I want to compare how close the sampled Gaussian distribution is to the Gaussian ...
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0answers
11 views

How to apply different values for input noises in GPML toolbox?

As you probably know, GPML toolbox accepts only one value for noise in both white noise covariance function and likelihood. Actually in my case, each input data has its own value for noise (16 ...
3
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1answer
94 views

How to transform one PDF into another graphically?

To understand what I mean, let's use two well-known distributions: the normal and lognormal ones. From the dataset point of view, if you take normally-distributed data and take their exponential, you ...
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1answer
12 views

Sampling Distribution question - Probability finding

Suppose it is known that 8% of males are color blind. In a random sample of 500 males, what is the approximate probability that at least 10% of them are color blind? I am doing review for finals ...
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1answer
49 views

Do the mean and standard deviation of the sum of independent normal random variables $X$ and $Y$ equal $\mu_X+\mu_Y$ and $sd_X+sd_Y$?

I was following with Chapter 4 of famous 'Statistical Inference 2nd ed' textbook (Casella, Berger) and discovered that if X is a randomly normally distributed variable, and so is Y, and both of them ...
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0answers
40 views

When I transform a distribution to apply a test that assumes normality, is the transformation “lossless”?

Many times we deal with data that do not conform to assumptions of normality and/or homoscedasticity/homogeneity of variance. Yet the reality is that almost all analyses benefit from improved the ...
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10 views

Maximization of a special log-likelihood function

I'm clear on how you found the likelihood function by multiply the pdf of all observations and then do the log to help when you derive. But here I don't understand the (2). Is it in a tobit censored ...
9
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2answers
137 views

Expectation of $\frac{X_1^4}{(X_1^2 + \cdots + X_d^2)^2}$

Let $X_1$, $X_2$, $\cdots$, $X_d \sim \mathcal{N}(0, 1)$ and be independent. What is the expectation of $\frac{X_1^4}{(X_1^2 + \cdots + X_d^2)^2}$? It is easy to find $\mathbb{E}(\frac{X_1^2}{X_1^2 +...
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0answers
13 views

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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1answer
52 views

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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1answer
32 views

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 ...
4
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1answer
49 views

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 ...
2
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4answers
350 views

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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17 views

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.
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1answer
14 views

Building a Regression Tree with one Gaussian Mixture Model at each node

I am trying to build a regression tree that outputs both a mean and a covariance matrix for each leaf of the tree. Ideally I would be able to have a Gaussian Mixture Model at each leaf. A first ...
3
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0answers
26 views

Wald confidence interval with delta method

Using the delta method, show that the Wald confidence interval for the logit of a binomial parameter $\pi$ is $$\log \left(\frac{\hat{\pi}}{1-\hat{\pi}} \right) \pm z_{\alpha/2} \sqrt{\frac{1}{n\hat{\...
3
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1answer
53 views

Relationship between Poisson, binomial, negative binomial distributions and normal distribution

When we have to define discrete counts distributions, we usually use : Poisson distribution, if mean = variance Binomial distribution, if mean > variance Negative binomial distribution, if mean <...
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Calculating the variance of a normal distribution given that it got value in a specific interval

Just wondering if it is possible to find the variance of x if it is normally distributed, given that x is in a certain interval(for example, above the mean value)? I know how to find the expected ...
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0answers
13 views

Threshold to segment count data following different distribution

I have a dataset D, wherein $ D = \{x_i, x_{i+1}, \ldots, x_n\} $. each data point in D is a discrete count data and since this is spatial data, one can expect dependence between contiguous data-...
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1answer
41 views

probability distribution function and quantile function for normal distribution in R

I've studied statistics before but I've forgotten quite a lot, but decided to pick it up again along with learning how to use R. I need help with this question: (I've translated from my Swedish book ...
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1answer
46 views

Distribution of the sum of the two dependent bivariate gaussian distributions and related questions

This is something I was thinking about and I decided to modify a question from a mid-term to ask this. Suppose $X_{1}$ and $X_{2}$ are two bivariate gaussian variables, decribed as $$ X_{i}=\begin{...