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Questions tagged [normal-distribution]

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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Normal Distribution Question Help

A car manufacturer introduces a new method of assembling a particular component. A sample of assembly times (minutes) taken after the new method had become established was: 27, 19, 68, 41, 17, 52, 35,...
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1answer
91 views

What is the distribution of the difference between two random numbers?

I have a big bag of balls, each one marked with a number between 0 and $n$. The same number may appear on more than one ball. We can assume that the numbers on the balls follow a binomial distribution....
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1answer
11 views

What happens to SD when there are more observations in two tails of a distribution? [on hold]

On considering the normal curve, I feel that as the tails get heavier, curve becomes flatter and hence SD decreases. But by formula, SD is deviation of observations from mean, more the number of ...
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0answers
8 views

Checking dataset distribution [duplicate]

While reading about the difference between Gaussian Discriminative Analysis and Logistic Regression here, I came across the idea that GDAs will have better performance on Gaussian data as it makes the ...
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0answers
19 views

Confidence interval to use when residuals non normal?

I have done regression but residuals not normal...When I take out outlier residual are normal.but the outlier is important data so I leave it in...In order to use my regression result do I reduce my p ...
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1answer
35 views

Variance of linear combination of Normal distributions

A company that develops software received an order for a service to be performed within a week and, in order to decide on the profile of the team of programmers to be used, it should take into account ...
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1answer
24 views

Distribution of the mean of normally distributed data

I have an exercise which requires the following: In water production, 1000 ml bottles are filled. The actual fill content is a random variable X. n = 20 bottles have been sampled (independent ...
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2answers
38 views

Tests of normality - qq and Shapiro-Wilk

I am new to the world of stats... My data had a log normal distribution, so transformed by log to get it nearer normal distribution. This is real-world data. From here I want to establish if my data ...
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2answers
20 views

Normal Quantile Function With a lower bound not equal to infinity

I was recently at a statistics competition and a question came up as follows: They drew a normal distribution with $\mu=7$ and the area between the values $7.75$ and $8.25$ equal to $0.12$. No other ...
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1answer
16 views

VAE derivation for Gaussian case

In Appendix B of the VAE paper by Kingma and Welling, they derive the KL divergence for the scenario in which $q(\textbf{z})$ and $p(\textbf{z})$ are both Gaussian. I do not understand this step: $$ \...
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0answers
17 views

How can you test dependence for non-Gaussian standardised residuals?

Let's say you fit an ARMA-GARCH model to financial data and find that the standardised residuals are non-Gaussian through the Kolmogorov-Smirnov test. These residuals have mean -0.002 and standard ...
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0answers
35 views

PDF of $\frac{(X_1-X_2)^{2}}{2}$ where X1 and X2 are independent standard normal [on hold]

I'm trying to find the PDF of $$\frac{(X_1-X_2)^{2}}{2}$$ where X1 and X2 are independent standard normal. Any hints on how to proceed with this?
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20 views

How to compare two sets of unequal data

I am doing a users perception research that compares experts opinions and novice users opinion for an application. The data collected was qualitative data from focus group. After analysing the ...
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0answers
72 views

Determine spread of data for non normal distribution

I've collected data from 12 sensors, the sensors are sampled at various times, mounted in one of three orientations and at different temperatures. I'm trying to determine the maximum and minimum ...
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2answers
39 views

How is the standard deviation in this coin tossing experiment calculated?

I'm reading Hypothesis Testing: The Basics, there is such an experiment: So, we have a coin. Our null hypothesis is that this coin is fair. We flip it 100 times and it comes up heads 51 times. Do ...
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0answers
25 views

How should I calculate mean CI - from raw data or mean values?

I have experimenatal data from medical industry. In the experiment 4 observations were weighted, each one 2 times for more precise measurement. As a final weight, a mean from each pair is reported. ...
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1answer
17 views

Just want a quick confirmation on a simple normal distribution problem

Given mean = 167cm, standard deviation is 3cm, a) When four are randomly selected, all of their heights will be greater than 170? b) When four are randomly selected, two will have heights smaller ...
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4answers
60 views

How to build a Bayesian Model to estimate the probability distribution of the parameters given the output?

I'm currently facing a new type of problem, and i have no idea how to solve it, so any suggestion will be really appreciated ! The problem is the following: I have a matrix of temperatures, depending ...
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0answers
17 views

Data smoothing through binning?

I have a small dataset of size n=26. ...
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1answer
29 views

Is this a reasonable coarse test for normality?

I'm interested in assessing if the marginalized posterior of a parameter obtained through a Bayesian MCMC process is "more or less normal". I use quotation marks because I'm not trying to asses for ...
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1answer
81 views

Gaussian Mixture: is this plot right?

I'm studying about Gaussian Mixtures and I decided to play around with it in Python, but I'm not entirely sure if I understand it fully. I generated some data, and then calculated the Gaussian ...
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0answers
6 views

is the PROCESS-test in statistics a parametric or non parametric test?

This might be a silly question. But my supervisor wants me to redo the analytical (spss) tests of my thesis, because my data is not normally distributed. I found that there is an alternative for the ...
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1answer
36 views

How to weight observations to transform a distribution into normal?

Suppose X is a variable which follows some distribution (non normal) then how to define $f(X(k))$ (f is some functions of the variable X) such that $$f(X)X$$ is normally distributed and $0\leq f(X(k))...
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Proving the normality of t statistics gathered from independence testing from unknown distribution

We are given a distribution P with unknown characteristics. Then, we repeatedly sample (without replacement) 2 samples from P. ...
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0answers
11 views

Finding variance normal distribution problem [closed]

Can anybode help me to understand this? I've tried to solve this problem but can't get the right answer. "For controlling purposes, 1000 packages of rice are sampled from the production output and ...
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1answer
45 views

How to to get normal distributed neural network output [closed]

I am trying to build a neural network that predicts a pair of latitude / longitude coordinates following a previous pair of latitude and longitude (highly simplified). The latitudes and longitudes ...
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1answer
234 views

How to generate samples of Poisson-Lognormal distribution

I would like to compute samples of the number of product purchased in a supermarket. I want to model it with a mixed Poisson lognormal distribution. Items purchased $x$ of a given consumer follow a ...
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1answer
49 views

What is the name for this classification algorithm?

Can you help me find the name of this classification method: Assume we have the following data: $n$ dimensional feature vectors we want to classify in two classes. We model the classes as two $n$ ...
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1answer
24 views

Conditional covariance of a multivariate normal vector

We know that the conditional variance of a multivariate normal vector $(X,Y)$ is the Schur complement: $$V(X|Y=(y_1,...,y_n))=\Sigma_{XX}-\Sigma_{XY}\Sigma_{YY}^{-1}\Sigma_{YX}$$ I have the intuition ...
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1answer
21 views

How to continuously rotate a bivariate normal distribution by changing its correlation matrix?

I want to create an animation in which a bivariate normal distribution rotate in xy plane by using matplotlib. I don't want to alter the variances in the two ...
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1answer
25 views

How do I determine the likelihood of a single measurement coming from a known distribution? [duplicate]

I have a set of 2000 numbers that form an approximately normal distribution, with a mean of about 0.24, and an SD of 0.06. These form an estimate of the population. I now have a single sample ...
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1answer
16 views

Location of “x standard deviation(s)” for multivariate normals

In 1D with scalar parameters $(\mu,\sigma^2)$, it is common to represent normally distributed data with error bars spanning $[\mu-\sigma, \mu+\sigma]$. In n-D with parameters $(\mu, \Sigma)$, where $\...
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2answers
47 views

Deriving the joint probability density function from a given marginal density function and conditional density function

We have a multivariate normal vector $\mathbf{X} \sim \mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\Sigma})$, where $\mathbf{X} = \left[ \begin{matrix} X_1 \\ X_2 \\ \dot\\\\ \dot\\\\ X_n \end{matrix} \...
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1answer
41 views

Log Transformation in R

I need to transform my not normal distributed data to normal distributed variables. Therefore I need to log-transform them. Log10(x+1) has not worked to create a normal distribution. Therefore, I want ...
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0answers
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VaR/inverse cdf of transformation of normal variables

I have the following exercise to solve as good preparation for an exam: NOTE: $VaR_p(X)$ = Value at risk = $F^{-1}_X(p)$ Consider the bivariate normal random vector $(X_1, X_2)$. The marginals are ...
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1answer
23 views

Find data points that deviate the most in 2D graph

I have a set of data points where X axis represents the percentage of disk space, and Y axis represents the memory used by an application. In general, higher the disk space, the higher memory it'll ...
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0answers
16 views

GMM model of the joint distribution from multivariate marginals

I have two multivariate Gaussian variables $X \sim \mathcal{N}(\boldsymbol {\mu}_X \in \mathcal R^d,\boldsymbol {\Sigma}_X \in \mathcal R^{d \times d})$ and $Y \sim \mathcal{N}(\boldsymbol {\mu}_Y \...
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0answers
27 views

Maximum entropy distribution on the hypercube

Given the first two moments, the maximum entropy distribution over $\mathbb{R}$ is known the be the normal distribution. What is the analogue for a distribution over $[0,1]$ given either only the ...
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0answers
44 views

Compute log-likelihood from sum of squares?

I have fit a 2D Gaussian to a surface in Matlab and need to compute the log-likelihood of this fit. Can One use the sum of squares between the Gaussian model and the actual surface to compute the log-...
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2answers
42 views

Why is the normal distribution a default choice for a prior over a set of real numbers?

I found this question without any context while preparing for a job interview. The only reason I can think of is that the Normal distribution's support are the real numbers. Why wouldn't we use a ...
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1answer
713 views

Why does MLE make sense, given the probability of an individual sample is 0?

This is kind of an odd thought I had while reviewing some old statistics and for some reason I can't seem to think of the answer. A continuous PDF tells us the density of observing values in any ...
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0answers
55 views

PCA: violation of the normal distribution assumption

I try to understand why normal distribution is an assumption for PCA and what might happens when it is violated. I found one answer on this plattform and a lot of different answers in literature. It ...
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2answers
106 views

variance of conditional multivariate gaussian

I was playing around with Gaussian Distributions on my machine and I was interesting in making a pretty plot. I wanted to show the distribution of $x_1$ if $x_2$ was given if $x_1,x_2$ were ...
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3answers
126 views

Fit data to parametric distribution

I have data with nice bell-shaped histogram PDF. However, the Normal distribution fitting (by calculating mean and variance) does not work as the figure below. My question is that if there are other ...
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0answers
44 views

Why that distribution is normal with those parameters?

Mi question is the following. I have two independent 2-dimensional normal distributions with the same mean vector and different covariance matrixes, lets say $X_1 \sim N_2( \mu, C)$ and $X_2 \sim N_2(...
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1answer
24 views

Choose one of two normal distribution that will give the probability of biggest value when sampling it

Suppose you have two (or more) normal distributions with different mean and variance. You can draw only one sample of only one of the available distributions. Your goal is to get the biggest value ...
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0answers
13 views

How to verify assumptions of a normal distribution? [duplicate]

I'm working with the iris data.I made a density plot And a qq plot For sepal Length.It looks Approximately normal With the left skew And a flat peak The points In the qq Plot Stay within The ...
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1answer
26 views

Value at Risk VaR with monthly return

The picture below shows the problem. I have tried to solve in this way: 0,001*1,88+2400*0,002 by following a formula in theory slides. But obviously there is a problem in that. Could someone help me ? ...
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0answers
21 views

When/why to use the normal approximation inside a vertical strip?

The Statistics book (Freedman, Piscani, Purves) has a section about using the normal curve inside a vertical strip. The introductory description is: Often, it is possible to use the normal ...
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38 views

Understanding sum of square deviations [duplicate]

Given $X_1...X_n\stackrel{iid}{\sim} N(\mu,\sigma^2)$ and $U=\sum_{i=1}^n (X_i-\overline{X})^2$, why is $U\sim\sigma^2 \chi_{n-1}^2$ ? And what would be the distribution of $V=\sum_{i=1}^n (X_i-\mu)^...