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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Anomaly detection: multivariate Gaussian distribution

I am trying to do anomaly detection on a heterogeneous dataset (There are unknown groups present in the dataset). I want to try multivariate Gaussian distribution based approach, but I was thinking of ...
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15 views

Scaling data constrained to be varying between a floor and ceiling set of values

I have data that range continuously between the values of 0 and 2, usually somewhere in between close to 1 on average. 0 is a "floor" and 2 is a "ceiling." The data describe more than one group of ...
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1answer
22 views

Finding maximum likelihood estimates of parameters of multiple normal populations

I've just started studying maximum likelihood and likelihood ratio tests. I've calculated the maximum likelihood of a normal population with unknown mean and variance. However, I've been given this ...
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1answer
14 views

Picking a probability distribution for observed intensities

I have an experiment that measures "intensity" (in this case, electron density of a molecule) on a grid. The values it gives are non-negative,. I'd like to write a likelihood for this observation ...
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0answers
12 views

Transformation of the covariate matrix within a Bivariate Normal Distribution

I have a Gibbs sampler (bivariate normal distribution) taken from a paper available here : Gibbs sampler available here : http://www.stat.wisc.edu/~mchung/teaching/stat471/lecture23.pdf. I can use it ...
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0answers
7 views

marginal posterior distribution in linear regression

Let's assume our posterior distribution looks like the bayesian linear regression posterior, \begin{equation} p(\mathbf{w}|D) = \mathcal{N}(\mu, \sigma) \end{equation} where \begin{aligned} \mu ...
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0answers
22 views

What should be the mean and variance of the bivariate normal distubution in the interval [on hold]

Condition: Suppose I have standard normal distibution X~N(0,1). But now I have calculate the mean and variance of the data which lies between a$<$X$<$0. Also explain me the casse of the ...
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1answer
64 views

Why do we lose conjugacy when assuming unknown $\mu$ and unknown $\sigma^2$ in a normal distribution?

Model: The following model corresponds to samples drawn from a Gaussian distribution with unknown mean and unknown variance: \begin{align} x | \mu, \sigma^2 &\sim \mathcal{N}(\mu, \sigma^2 )\\ ...
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1answer
37 views

Asymptotic distribution for moments of gaussian distribution

Is there a way to find the asymptotic distribution for the moments of Gaussian distribution? More specifically, say you have $X_1, ..., X_n \sim N(\mu, \sigma^2)$. For a moment $m_{n, k} ...
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0answers
24 views

LS vs MLE for Gaussian Conditional Random Field estimation

Is there such a thing as Least Squares estimation for the conditional mean and covariance of a conditional gaussian random field? I'm looking at this paper by Wytock and Kolter 2013, in which they ...
3
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1answer
30 views

Possible to morph a bimodal distribution into a normal distribution slowly?

Is it possible to slowly turn a bimodal distribution into a normal distribution slowly by shifting some parameter K? The reason I want to do this is because I want to conduct a scenario analysis and ...
3
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1answer
54 views

Generate random correlated categorical variables

Lets say I want to generate 100 observations of 2 likert scaled, normally? distributed variables with 10 categories (1-10) and a pearson correlation of f.e. ~0.8. I am aware that using pearson ...
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0answers
10 views

Normal Probability Plots in Excel [duplicate]

I am a student in an introductory statistics course and I am working on my project regarding number of hours I spend working my job a day. We went over normal probability plots and I am now trying to ...
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0answers
12 views

Two random variables each come from different distributions. How do I calculate P(X1>X2)? [duplicate]

I have X1~N(55,2) and X2~(48,4). Is there a simple math formula for calculating the probability that X1>X2? Thanks!
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0answers
31 views

expectation of a random variable [closed]

Recently a question has made my life difficult. It might be easy to be solved but for me is difficult. Assume X Is a random variable that follows distribution F. Now I am interested in following ...
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2answers
82 views

Detecting Bimodal Distribution

I have histograms of audio signals where they have bimodal "normal" distribution. What I want to do is to detect these subpopulations inorder to have a threshold, this is meant to divide the values ...
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0answers
19 views

How can I calculate $$\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right) \left(\frac{w-a}{b}\right) f(w; \mu, \sigma²)\,\mathrm dw$$ [migrated]

Suppose $\Phi(\cdot)$ is the cumulative distribution function of the standard normal distribution and $f(\cdot; \mu, \sigma²)$ is the density of the normal distribution with mean $\mu$ and standard ...
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0answers
38 views

Polynomial transform of a Gaussian Random Variable

I have been trying to find how the PDF of a polynomial transform of a Gaussian Random Variable could be found. Eg: If \begin{equation} \ X\sim N(\mu,\sigma^2) \end{equation} Then what would be the ...
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1answer
26 views

Multiplication of two random distribution

I am trying to find the resulting PDF , when two random functions are multiplied. First function obeys normal distribution and second function obeys cauchy distribution. Can anybody tell me how to ...
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1answer
31 views

Constructing Bayesian model for randomly picked points from a sine wave

I am trying to apply some data analysis on data which is generated by picking points from a sine wave with some noise added in. I am purposefully ignoring the time dependence, so just collecting data ...
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1answer
40 views

Show the shortest confidence interval of a normal distribution

I'm having trouble formally showing a problem I have been given. It goes as so: Show that among all $(1-\alpha)*100$% confidence intervals of the form ...
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0answers
14 views

What factors influence the point at which a sampling distribution is said to be nearly normally distributed?

What factors influence the point at which a sampling distribution is said to be nearly normally distributed? *Note that the answer I am looking for is not sample size. I am asking what decides how ...
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45 views

When to Use Sampling Distributions And When to Use Regular Probability Distributions [closed]

Why/When would it be better to use Sampling Distributions such as the Sampling Distribution of the Sample Mean and why/when would it be better to use a Probability Distribution (such as Beta, ...
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Normal learning - multiple signals

I'm having trouble with the exercise below. I know that $E(η_t|z_t)= E(η_t) + [Cov(η_t,z_t)/Var(z_t)](z_t - E(z_t)) $ but still can't show 'b'. I imagine I'm missing something very simple... Can ...
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0answers
15 views

Test statistic and C.I. for population proportion

I'm doing a test statistic and C.I. for population proportion. Can someone explain to me what are assumptions coming from hypergeometrical distribution directly to normal distribution? As I ...
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2answers
75 views

Calculating $\overline{X}$ and $S(X)$ for a truncated Normal distribution

I have the following dataset which appears to be normally distributed but is truncated at 0. If I ignore the values which are 0 I get an even better distribituion. I would like to conclude that ...
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1answer
25 views

Explanation of an example of the Bayes Estimator

In section 4.4 of 'Introduction for Machine Learning' by Ethem Alpaydin the following example of estimating a prior density us given: For example let us say that we are told that [the random ...
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1answer
73 views

How many individuals must be measured to determine the true mean?

I saw this was asked earlier, but I also have the same question. This was the question: "Anatomy: The human height is the distance from head to toe. When populations share a genetic background and ...
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1answer
43 views

Normal distribution (R)

This is the graph of my variable after the $\sqrt[3]{x}$-transformation. After the transformation, I ran a Shapiro test and obtained a $p$-value of $0.004262$. Is it possible my transformed variable ...
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7answers
235 views

How to judge if 5 point Likert scale data are normally distributed?

I have read that the t-test is used when the population is normally distributed. How can I determine if my data are normal given that I am using 5-point Likert scale with a sample size of 100? What ...
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1answer
60 views

Empirical Rule. Is it applicable/usable in this case?

So I ran in this problem: I have to test whether Empirical Rule is applicable. Proportions I got is 73%, 94,7% and 99.1% (within one, two and three standard deviations). I'm worried about 73%. This is ...
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1answer
74 views

Obtaining conditional distribution from mixed model

Suppose you have the following mixed model: $$y_{it} =X_{it} \beta + Z_{it}b_{i} + u_{it} \tag{1}$$ where $y_{it}$ is the response for a subject $i$ and time $t$, $X_{it}$ is a vector of features, ...
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Reasons for data to be normally distributed

What are some theorems which might explain (i.e., generatively) why real-world data might be expected to be normally distributed? There are two that I know of: The Central Limit Theorem (of ...
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1answer
108 views

Why kurtosis of a normal distribution is 3 instead of 0

What is meant by the statement that the kurtosis of a normal distribution is 3. Does it mean that on the horizontal line, the value of 3 corresponds to the peak probability, i.e. 3 is the mode of the ...
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0answers
11 views

Reasons for data to be normally distributed [duplicate]

What are some theorems which might explain (i.e. generatively) why real-world data might be expected to be normally distributed? There are two that I know of 1) The Central Limit Theorem (of ...
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1answer
32 views

confidence interval of a difference of variables

Let's say I got two samples from two unknown random variables: $(x_i), (y_i)$ At this stage I don't know (or don't want to assume) that they come from a similar process or not. I want to compute a ...
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1answer
245 views

Probability distribution for a noisy sine wave

I'm looking to analytically calculate a probability distribution of sampling points from an oscillating function when there is some measurement error. I have already calculated the probability ...
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1answer
141 views

What distribution does $\ln(x)$ have when $X$ is normally distributed?

It is known that a variable $X$ has a log normal distribution if $\ln(X)$ is normally distributed. What is the distribution of $\ln(X)$ if is $X$ is normally distributed? Can someone provide a ...
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16 views

Understanding Multivariate Normal Distribution in simple terms

While reading about the proc Tcalis procedure in SAS for SEM, I came across the statement: "For maximum likelihood (default) and generalized least squares ...
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0answers
16 views

Are my data normal? chi-squared for goodness of fit [duplicate]

I have been tasked with determining if my observed data follow a normal distribution. With 119 observations (continuous data from -4 to 4), I was able to create a histogram with 25 bins, and upon ...
3
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1answer
88 views

Sum of Gaussian is Gaussian?

As a newbie in probability, I am recently cleaning my understandings about Gaussian distribution. I know that If $X$ and $Y$ are jointly Gaussian, then $aX+bY$ ($a$ and $b$ are both constant) is ...
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1answer
142 views

Why stock prices are lognormal but stock returns are normal

Except for the fact that returns can be -ve while prices must be +ve, is there any other reason behind modelling stock prices as a log normal distribution but modelling stock returns as a normal ...
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1answer
22 views

Trying to Find Article by Tukey

I am trying to find a commonly cited paper by John Tukey published in 1960 called "A survey of sampling from contaminated distributions", from a monograph(?) called "Contributions in Probability and ...
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2answers
135 views

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
18 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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0answers
47 views

Square root of number of counts vs 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
50 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
46 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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1answer
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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 ...