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The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is one of the most important distributions in statistics. Use the [normality] tag for asking about testing for normality.

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Convert datetime in dataframe to seconds

Below is the output of [mydataframe].info() ...
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1answer
34 views

Are my stock returns non-normally distributed?

Hello stats community, I have a Q-Q plot for my stock returns with a sample of n=262. I drew the plot with qqnorm and qqline(qtype=8). Most of the returns, except for 3 outliers, tend to follow the ...
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16 views

When the T stat suggests the null hypothesis should be rejected for a one tail test, but accepted for a two tail test [duplicate]

I would like to ask a question about interpreting the results of a t-test. I am sorry if the answer is obvious and ask you to excuse me in advance. What happens in a situation where: t-stat = 1.91 ...
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21 views

Comparing probabilities generated by two different normal cumulative approximations [on hold]

Suppose I have two ways of approximating cumulative normal probability and I want to compare whether the two methods are equivalent. The most obvious way to go about it would be to have a bunch of ...
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12 views

How to correctly use the z-transformation in deriving the normal pdf from the binomial

I have understood that the Normal distribution may be motivated by considering the Binomial distribution for large N. I wished to create a geogebra file but encountered a problem I'd not thought of ...
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14 views

Entropy of a mixture of Gaussians

I need to estimate as fast and accurately as possible the differential entropy of a mixture of $K$ multivariate Gaussians: $$ \mathcal{H}[q] = -\sum_{k=1}^K w_k \int q_k(\textbf{x}) \log \left[\sum_{...
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4 views

Acceptance rejection with Halton sequence as RNG

I am coding various normal random variable generators, one of them being the acceptance rejection method: ...
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1answer
35 views

Find a realistic distribution scenario for requests

For a loadtest I have to figure meaningful numbers for the maximum number of requests per hour and minute. The only thing I have is the number of requests per working day (which is a timeframe of 14 ...
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5 views

Help with computing message on TrueSkill factor graph

I want to better understand the step for calculating the message from the game factor $h_{g}$ down to the difference variable $d_g$ on the TrueSkill factor. Such message is shown in the Rasmussen's ...
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13 views

Estimator of (left-)censored normal distribution when mean>>std

Suppose there is a left-censored normal distribution, and we know there is a total of $m$ samples, for which we know $n$ of them. I am trying to estimate the mean and variance of the underlying normal ...
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27 views

Parameter which would make a Gaussian Distribution 'equal to' or 'closely fit' another Gaussian Distribution

I have these two Gaussian distributions: fX1 ~ N (10, 12) 12 is the variance and not standard deviation ...
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3answers
1k views

Are all continuous random variables normally distributed?

All the time I see examples of the normal/Gaussian distribution with continuous random variables. So my question is do all continuous random variables have a Gaussian distribution?
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8 views

Conditional expectation of RVs under truncation-based stochastic signal release?

Suppose $z\sim N(0,1)$ and $x\sim N(\gamma z, 1)$, where $\gamma$ is a known sensitivity parameter. That is, $x=z+\epsilon, \epsilon \sim N(0,1)$ where $\epsilon$ is exogenous. Further, suppose there'...
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26 views

Calculating Variance for a Normal Distribution [closed]

I want to add noise to a given time series of data. The noise is to be generated using a distribution technique. For example for an interval of 10 min I have 60 entries which sum upto say 13643Kw. ...
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0answers
9 views

($L_2$) distance for noisy data

I'm given a subspace $V$ and a set of $n$ corrupted observations $\tilde{x}_1 = x_1 +\epsilon_1,...,\tilde{x}_n = x_n + \epsilon_n \in \mathbb{R}^D$. Assume $D$ is large and that $\epsilon_i \sim N(0, ...
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17 views

CLT for different but independent random variables [duplicate]

Is the Central Limit theorem still applicable if we consider a sum of independent but different random variables? (Each with finite mean and variance) Is there some theorems about this ?
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1answer
31 views

Can I assess the relationship between a normally and non-normally distributed variable?

My study is related to the visual attractiveness of route-plans in a logistics context. In practice, route-plans are rejected based on the fact that they "do not look nice". I have conducted an ...
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14 views

Extrapolating maximum (x,y) values and initial slope of non-linear fitted glm curves

I have plotted 8 curves using a log-link Gaussian model, y=ax exp(bx)+ϵ, for my data. I couldn't find a way extrapolate the maximum (x,y) from each of the fitted curves, of which I intend to use for ...
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1answer
72 views

When we take draws from a normal distribution what are we drawing? [closed]

As I dig deeper than surface level in probability I'm starting to ask more questions I never thought about before. There are a bunch of intertwined concepts that are quickly becoming confused in my ...
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0answers
19 views

Fit Correction on known distributions

I'm looking for a way of correcting a linear fit through data. The scenario is the following: In red you have data points, they are based on uniformly distributed points on the black straight line ...
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0answers
34 views

Generating random data that satisfies two conditions

I am looking to generate a synthetic set of data. For clarity I will use a simple example and then elaborate. Suppose that I would like to create a set of data concerning the color and size of a ...
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0answers
82 views

Fourier transform of a Gaussian process

I would like to discuss and ask a question regarding the Fourier transform of a Gaussian process, if it makes sense. For that purpose, let me describe the following situation. Let $z(s)$ be a ...
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1answer
32 views

From log-normal parameters, to normal parameters

from the following log-normal fitting function (https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html), I get the parameters [s, loc and scale]. How can I use them to get the μ ...
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1answer
14 views

Errorbar determination for non gaussian distribution

Suppose I have a data set which has a nice Gaussian distribution f(x), then I can "summarize" as Mean{f(x)} +- Std{f(x)} Where std stands for standard deviation. However, If my data does not look ...
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1answer
24 views

GLMMs, stable isotope distribution analysis

I am currently working with a set of samples of stable isotopic concentrations obtained from a group of individuals. I am trying to process this data through a glmm() from the package lme4 to ...
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1answer
39 views

Proof of the standard error of the distribution between two normal distributions in A/B testing

Classic A/B test suppose that there are two independent experiments, each with $n_1$ and $n_2$ observations, for which we are interested in an event following a binomial distribution $\mathcal{B}(n_1,...
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8 views

Training Gaussian Restricted Boltzmann Machines with Noisy Rectified (nrelu or ssu) linear hidden units

I'm not sure how to implement this architecture. I'm following this thesis http://www.cs.toronto.edu/~ndjaitly/Jaitly_Navdeep_201411_PhD_thesis.pdf (pag 17-19) or this paper http://www.cs.toronto.edu/~...
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3answers
270 views

A question about Histogram-to-distribution transformation

I have done a simulation with 1 million runs on Matlab. I have got a histogram for this. Using Matlab command hist(X), (where X is the 1 million samples as results ...
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1answer
29 views

Why don't I see my points on cullen and frey graph

I have a set of data of 5 members. based on some previous questions , I was expecting to see where my actual points are located on the graph. in my case I see the theoretical but not my points. just ...
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0answers
19 views

Discrete version of multivariate normal distribution

Let's say that I have a 2d map, and I would like to explore around my house. Drawing samples from a bivariate gaussian centered at the x, y location of my house makes sense, as I don't want to stray ...
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1answer
24 views

Statistical time series analysis using Percentile and Empirical Rule

I analysing time-series to see the range of an asset. I have data for GBPUSD so i could only analyze this so far. I have used both empirical rule and percentile. Of course they give different ...
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1answer
37 views

Gaussian mixture as a prior of gaussian

I'm curious what would be the posterior distribution having prior dstribution as a mixture of two guassian with the likelihood dist as a gaussian. In other words: Likelihood: $p(x|\mu,\sigma) = \...
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2answers
194 views

What is the distribution of min{0,X} when X follows some general normal distribution?

What is the distribution of $\min\{0, X\}$ when $X$ follows some general normal distribution?
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2answers
52 views

why does the distribution of height follow Normal Distribution?

The height of a class of students in a school is said to follow Normal Distribution. We know that the domain of a random variable that follows Normal distribution is said to range from minus infinity ...
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24 views

Fitting a Multiple Gaussian Peaks to a Smooth Curve to Calculate Resolution in R

I used interpolation to fit a smooth curve to my data. I did this in order to visualize peak and valley regions. My goal is to calculate resolution (separation between peaks). I have peak to valley ...
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2answers
448 views

Is a distribution still considered right-skewed if the majority of responses are zero?

i have a distribution in which the majority of cases take the value of zero and then there are a few (perhaps 10%) with values of 1,2 or 3. would this distribution still count as right skewed even ...
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1answer
17 views

Is there a most accurate statistical model or they are used for different distribution? [closed]

I know empirical rule and use it for a normal distribution data. I know percentile and i use it too and love it. But are there any other statistical models? Or what model gives the most accurate ...
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1answer
41 views

Normal approximation to Poisson: With Continuity Correction the Approximation Seems Worse

This is Exercise 3 in Section 6.3 of Probability and Statistics, 4th edition, by DeGroot and Schervish: Suppose that the distribution of the number of defects on any given bolt of cloth is the ...
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21 views

Writing syntax for bivariate survival censored data to fit copula models in R

Am required to fit copula models in R for different copula classes particulary the Gaussian, FGM,Pluckett and possibly Frank (if i still have time). The data am using is Diabete data available in R ...
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1answer
21 views

The ideal transformation for a non-normal variable

The dependent variable seems to resist to become normal. Here I have depicted the probplot of the variable in three situations. ...
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1answer
25 views

probability of a difference between two sampling means of two populations

If I have two normally distributed populations $\mu_1 = 7, \sigma_1 = 0.5$ and $\mu_2 = 6.6, \sigma_2 = 0.5$ and I sample each of the populations say with 10 samples each. If I want to work out the ...
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1answer
21 views

Normal Distribution: Is it made with replacement or without replacement?

I am confused about how a normal distribution is drawn. Are the elements drawn with or without replacement?
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2answers
38 views

Does the distribution of each mixture components have any information of the margins of the variables?

I just start working with Gaussian mixture models and I just confused about some information, which I really would like to make sure that I understand the model very well. A Gaussian mixture model ...
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2answers
288 views

What is the ratio of a N[0,1] and U[-1/2,1/2]?

I have come across a problem where I can reasonably assume that the numerator is a uniform distribution of the type U[-a,a], i.e., centered on zero, and the denominator is N[0,b]. This seems to be ...
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0answers
22 views

obtaining a distribution from the sum of normal distributions

We are given that $Y_i$ ($i=1,2,3...10$) is an independent random sample from a $N\sim(-1,4)$ distribution, and that Q is given by: $$Q=\frac{1}{400}\Bigl(\sum_{i=1}^{10}(Y_i +1)\Bigl)^2$$ The ...
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0answers
55 views

Does Gaussian mixture models always assume normality distribution?

Suppose that we are given a data. Then, one needs to select the best fits models that approximate the distribution of the data. The most widely used mixture model is a Gaussian mixture model. In this ...
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0answers
29 views

Checking normality of a dependent variable and choosing statistical test

I am working on data comparing a dependent continuous variable in 2 groups. In one group, the variable is a constant while the variable appears normally distributed in the other group. Should I ...
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0answers
48 views

Analytic proof of an intuitively evident fact about normally distributed variables

Let $X,Y\sim N(m,1)$ be identically distributed random variables, $m>0$. An observation $(\hat X,\hat Y)$ is obtained from $(X,Y)$ by one of two rules: $(\hat X,\hat Y)=(\lambda X,Y)$ or $(X,\...
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1answer
74 views

Does confidence interval for odds ratio assume log-normal distribution?

The formula floating around for calculating 95% confidence interval of an odds ratio is: e^(log(OR) ± 1.96 x sqrt(1/a + 1/b + 1/c + 1/d)) Does one need to ...
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0answers
11 views

Compound Normal Distribution [duplicate]

Suppose a random variable can follow one of the two normal distributions. With probability $p$ it follows $N(m_1, s_1)$; with probability $1-p$ it follows normal distribution $N(m_2, s_2)$. Is the ...