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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Transformation Chi-squared to Normal distribution

The relationship between the standard normal and the chi-squared distributions is well known. I was wondering though, is there a transformation that can lead from a $\chi^2 (1)$ back to a standard ...
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1answer
12 views

Is a normal process mean reverting

A normal process has a lot of outcomes around the mean and then fewer and fewer outcomes away from the mean. From this, can we conclude that a normal process reverts to the mean whenever it gets a ...
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13 views

Square root of number of counts, or standard deviation of the mean?

I'm doing an experiment in radioactivity, where I measure the number of counts in a given time interval when a radioactive source is placed in front of a detector at a fixed distance. I repeat 3 times ...
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2answers
31 views

Draw a histogram with normal distribution overlay

I was asked to draw a histogram with normal distribution overlay over our data and I'm quite a noob in statistics and require help in this. Our data is an array of floating point values, and the ...
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1answer
36 views

Generating a Laplace prior from a normal random variable with Rayleigh standard deviation.

I read on Wikipedia Laplace distribution that the following is true: If $X|Y \sim N(\mu,\sigma=Y)$ with $Y \sim \text{Rayleigh}(b)$, then $X \sim \text{Laplace}(\mu, b)$. However, there doesn't seem ...
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21 views

understanding U-statistics calculation in directional statistics

I'm trying to work with U-statistics as described in Mardia and Jupp's 2000 book Directional Statistics (2). Specifically pages 220-2 there is a test for the equality of concentration parameters. The ...
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0answers
53 views

normality testing

What is the best method for testing for normality? I have a smaller data set today (30 in each group) and on the histograms none of them look normally distributed at all, whereas with the skewness ...
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1answer
19 views

How to derive quantiles of a non-standard normal distribution [duplicate]

Let X = [11.17, 9.52, 10.69, 9.84, 10.84, 9.88, 10.28, 12.23, 8.49, 10.79] be a normally distributed data with mean = 10.37 and standard deviation = 1.02. How to determine the corresponding value to ...
2
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1answer
64 views

t test with log transformation

One of my variables to be compared in a t-test is normally distributed, while the other is non-normally distributed. What test should I use? I thought I should do a reflect log10 transformation on the ...
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0answers
7 views

Wavelet transform of Gaussian function [on hold]

What is the wavelet transform of Gaussian function? Any continuous wavelet can be used.
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1answer
192 views

Area within a given number of standard deviations from given mean

I have a variable with mean value of 18.85 and standard deviation of 1.45. I want to define the area that is covered by 1.45 standard deviations left and 1.45 standard deviations on the right side ...
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2answers
39 views

Why do we estimate population parameters using statistic?

I had been studying statistics, I have a doubt that I couldn't find the answer of. Its related to estimating population parameters using statistic. Suppose we have a population size of 10000, we want ...
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0answers
20 views

Sampling from a portion of the normal distribution?

I have a a conditional distribution $p(X_1 | \theta) \propto MVN(\mu, \Omega) \pi(X_1)$ where $X_1=[x_1, x_2, \dots, x_n]'$ and $\pi(X_1)=1$ when all $x_i \in [0,a)$ and $0$ otherwise. Is there any ...
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0answers
24 views

How to check $H_0$ hypothesis using Pearson's criteria?

How to check hypothesis by using Pearson's criteria, that $H_0:$ random variable $X$ is normally distributed given that $k=7$ (count of intervals) and $\alpha=0.1 $ (significance level). I do ...
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0answers
15 views

Bimodality after Box-Cox Transform [closed]

I have a data set that I need to transform to make it look more normal. This data will not be modeled using linear regression since it is not possible to measure response data. Instead, we are using ...
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0answers
34 views

Marginalizing product of multivariate normal distributions

How should I marginalize $F_{i}$ from the following probability distribution $$p(y_{i}|F_{i},\alpha, \Lambda, \Phi, \Sigma) = N(\alpha + \Lambda F_{i}, \Sigma)$$ in order to obtain ...
2
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1answer
31 views

Sampling according to a difference of two normal distributions

Assuming that I have two normal distributions $p_1(x)$ and $p_2(x)$ and I can draw samples efficiently from them. Now, I can easily draw samples from $p(x) = 0.5 p_1(x) + 0.5 p_2(x)$ by with ...
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1answer
24 views

Hypergeometric approximated Normal/Gaussian distribtuion

A large lecture theater has 270 seats, 24 of which can accomodate left-handed students. Suppose it is known that 14% of people are left-handed. One class held in the theater has 205 students. (a) ...
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28 views

Multivariate normal with singular covariance

I'm an undergraduate student. I read about multivariate normal distribution in hogg and craig. And i wonder why the covariance is allowed to be positive SEMI-definite. I read this Normal distribution ...
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11 views

Normalisation formula applicable to one or more data items

I've created a recurrent neural network, to which normalised values are passed as inputs. The normalization formula is: $$\tilde{x_{i}} = \frac{1}{1+exp(-\frac{x_i-\bar{x}}{\sigma})},$$ where ...
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17 views

Calculate pdf of complex model

I'm trying to model the distribution of effects of mutations (let's call it s) in evolution but I'm stuck in generating the probability distribution function (pdf) for my model. So, my model is a ...
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1answer
58 views

What is the probability that a girl is taller than a boy, with boys ~N(68, 4.5) and girls ~N(62, 3.2)?

"Given that boys' heights are distributed normally $\mathcal{N}(68$ inches, $4.5$ inches$)$ and girls are distributed $\mathcal{N}(62$ inches, $3.2$ inches$)$, what is the probability that a girl ...
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1answer
66 views

Gaussian is conjugate of Gaussian?

Someone told me that, Gaussian distribution is conjugate to distribution because a Gaussian times a Gaussian would still be Gaussian distribution ? Why is that ? Say the following situation: $X\sim ...
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22 views

Fitting multiple normal distributions to sample data

I have a data set of (time, action)-tuples. Actions are typically performed at approximately the same times every day, and depending on what the action is it may be done multiple times per day. If I ...
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1answer
24 views

z-score and Normal Distribution

I have what is probably a pretty stupid question but for whatever reason I have not been able to find an answer so here goes.... It's my understanding that a z-score can only be calculated and ...
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1answer
27 views

Choosing Variance for Gaussian Prior

I'm relatively new to bayesian inference, and was trying to apply a bayesian model in a real-world scenario. Let me describe the model in brief: We have $N$ i.i.d. random variables $D =(X_1, X_2, ...
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8 views

Find Points that Break a mutli-valued Relationship

I am looking for a suggestion on how to answer a question, or what to read more about. I am sorry if I do not sound professional, I am not. First a contrived example. I have a table of 50 states in ...
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49 views

How to transform continuous data with extreme bimodal distribution

Is there a way to transform a continuous predictor variable (grant) that has a bimodal distribution into a normal distribution (see density plot below)? I have tried log(x+c), z-score and inverse ...
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15 views

Is it reasonable to utilize z-scores

I have empirical observations to be compared with discrete distributions of random values (generated according to random models). The shape of my random distributions is not normal(according to ...
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1answer
49 views

Fitting a Gaussian to a histogram when the bin size is significant

I'd like to fit a Gaussian to some experimental data that is binned (the binning is a result of the physical limits of the device). Importantly, the bin size is significant enough that the gaussian ...
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0answers
22 views

How to find normal quantiles?

A social psychologist interested in eating behavior wanted to divide students into four groups based on their eating proclivities. The four groups were those who were restrained eaters, moderately ...
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2answers
30 views

When to use a multivariate normal distribution?

I was reading Bayes Point Machine example from infer.net: http://research.microsoft.com/en-us/um/cambridge/projects/infernet/docs/Bayes%20Point%20Machine%20tutorial.aspx The problem is when we have ...
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3answers
15 views

Error Propagation

I come from a physics background where the only error propagation I've dealt with was in the lab using the simple formulas found here: ...
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1answer
53 views

Heckman 2-step Error Assumption

first question on StackExchange; thank you for having me. I am trying to really nail the intuition for the Heckman sample selection model. One little thing that is bothering me is the assumption ...
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2answers
80 views

Confirmation of normality using residuals from an linear regression

95% of my residuals from an linear regression lie within 2 standard deviations of the predicted values. Is this enough to confirm normality or could any other distributions have 95% of residuals that ...
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1answer
29 views

Noise removal from a dataset with a know distribution

If I have a dataset where it's points are drawn from a known distribution(For example a normal distribution) due to some noise the histogram doesn't reflect such a behavior (not necessarily skewed) ...
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26 views

p-values, prior probabilities

I've got a set of N normal independent normal distributions, each representing a signal. I also got a new data sample, a vector $v$ of size Nx1. Now let's say I compute the p-value using the ...
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22 views

Existence of a specific linear combination of independent random variables (stochastic representation of the flexible skew normal)

Suppose to have two standard normal variables $X$ and $Y$. I would like to find something as $Y= aR+\sum_{i=1}^k b_kC_k$ (1) (k can be 1,2 or whatever) where $a,b_1, \dots , k$ are appropriate ...
2
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1answer
45 views

Why make the distribution of a variable more symmetric?

One of the goals of re-expressing data values is to "make the distribution of a variable (as seen its histogram, for example) more symmetric. My question is: why is more symmetric data better for ...
2
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1answer
45 views

Weird pdf of a quadratic function of a N(0,1) variable: miscoding or big rounding error?

I would like to calculate the pdf of a random variable y defined by : y=c+b*x+a*x^2 The pdf is a non-central chi-squared distribution. For a>0, it should be equal ...
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1answer
37 views

Correlated random draws with graph structured correlation

I have a problem where I have a graph structure, such that some nodes are connected to other nodes i.e. we have an adjacency matrix of size n*n with a 1 corresponding to a connection and 0 otherwise. ...
2
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2answers
60 views

What is the mean of this exponential random variable?

I have read a paper that says that the following is exponentially distributed $$ Y= \bigl| \sum_{i=1}^n \gamma_i^{-\frac{1}{2}} h_i \bigl|^2$$ where $\gamma_i$ are non-negative constants and ...
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2answers
220 views

Is data distributed as a Gaussian?

I know there are methods to check whatever the observed data DOES NOT follow a Normal distribution. I'm thinking about chi-square test, Anderson test etc. Is there any function/test/metric which says ...
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0answers
45 views

Multivariate normal distribution

I am not able to figure out how to derive this.Kindly explain this step.
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1answer
25 views

Confused by notation for normal distribution

In my statistics course, we were taught that the normal distribution function can be expressed as $f(x; \mu, \sigma).$ However, I also sometimes see it as $X \sim N(\mu, \sigma^2)$ Are these the same? ...
2
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2answers
65 views

Re-estimating a probability distribution with additional priors

I have a 3D dataset with at least millions of data points (scatter events from atoms, approximately Gaussian). I am modeling this data with a Gaussian Mixture Model. The usual approach would be to ...
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0answers
30 views

Why there is no uniform prior for Box-Cox Power Transformed Normal Models

I am trying to get intuition why uniform prior like below will not work for the box-cox model. Box-cox model: $y^{(\phi)}_i \sim N(\mu, \sigma^{2})$ where $y^{(\phi)}_i = (y^{\phi}_i-1)/\phi $ if ...
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33 views

Cumulative Distribution Function For Normals

Suppose $X_1$ and $X_2$ are $N(0,1)$ random variables such that $X_2=-X_1$ if $|X_1|<1$ and $X_2=X_1$ otherwise. Obtain the cumulative distribution function of $X_1+X_2$ represented in the form(s) ...
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1answer
16 views

Variance of precision in conjugate prior

How can I calculate the variance of the precision in a normal distribution, knowing I used a conjugate prior?
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1answer
31 views

Probabilistic comparison of two mixture models?

Given two gaussian mixture models (GMMs) with different degrees of freedom, is there a way to determine the probability that one is generated from the other? That is, can we give a probability to the ...