The normal, or Gaussian, distribution is a symmetrical bell-shaped curve that is defined by the mean and standard deviation. Parametric statistics tests require the population to be normally distributed. A sample distribution that is normally distributed is used to assume that the population ...
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26 views
Shapiro test on replicated values
I have a distribution of frequencies (1000 data points) expressed as %. The list of data looks like this:
3.10%
1.80%
1.70%
1.70%
1.60%
1.60%
1.50%
I would like ...
0
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0answers
75 views
Understanding Naive and Multivariate Gaussian Classifier
Thank you for checking this question out.
I am trying to understand how to use the multivariate gaussian classifier.
To introduce you better to my problem, I will show how currently I classify data.
...
2
votes
0answers
37 views
How can I visualise a distribution that is univariate normal but bivariate non-normal?
I used the MATLAB code written below to create the following probability density function. It creates the familiar hill-shaped distribution.
I'm interested to see (whether via MATLAB code or just ...
0
votes
0answers
17 views
Estimating sparse inverse covariance matrix in high dimensional data
I am trying to estimate the graph in very high dimensional data, I mean with million nodes. Up to now all the papers that I have found, they are limited to few thousands.
All of them like graphical ...
2
votes
0answers
42 views
When data has a gaussian distribution, how many samples will characterise it?
Gaussian data distributed in a single dimension requires two parameters to characterise it (mean, variance), and rumour has it that around 30 randomly-selected samples is usually sufficient to ...
0
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0answers
30 views
pdf of multivariate normal distribution
I have a question concerning some sentences in the book Structural Equations with Latent Variables (Bollen) at page 132 (bottom) and page 133 (top) regarding the pdf of the multivariate normal ...
0
votes
1answer
31 views
Confusion related to minimization of a gaussian likelihood function
I have this confusion related to minimization of gaussian likelihood function. The negative of the log likelihood of gaussian distribution is
$-\log \det(Q) + \text{tr}(SQ) + \lambda||Q||_{1}$ where ...
0
votes
0answers
51 views
Minimum enclosing Gaussian
Given two weighted Gaussians with arbitrary weight, mean and variance, what is the parameters of the minimum enclosing Gaussian? The mean and variance should be chosen such that the weight is minimum ...
3
votes
1answer
75 views
How to test for normality of growth disturbances in chemo treatment?
I'm a med student, conducting a retrospective analysis of weight/growth disturbances during chemo treatment.
I wonder, if I should:
assume, that growth is a variable normally distributed across the ...
1
vote
1answer
46 views
Calculating the std dev of a 30 team league with each team having a 50% chance of winning
I just want to preface this with the fact it is not a home work question. I am also not a stats person so I am not sure even how to start with calculating this, what it is called or where to look. ...
-1
votes
0answers
47 views
This game consists of rolling two dice, one 8-sided and one 12-sided. you will roll the dice 10 times to complete the game
This game consists of rolling two dice, one 8-sided and one 12 sided. You will roll the dice 10 times to complete the game. Each roll is considered a win, if you roll a total of 6 or less. ...
0
votes
0answers
20 views
Is the t-test really robust to shape of distribution? [duplicate]
Can I use the t-test to compare means between groups (N=300) if data is not normally distributed?
0
votes
1answer
44 views
Fit of a normal distribution to a one-dimensional dataset in R
I've got a set of (continuous) values from a measurement, where each object should be either positive or negative, and I know that the values of the "negative" objects should be approximately normally ...
3
votes
0answers
38 views
Ratio of sum of Normal to sum of cubes of Normal
Please help me to find the limiting distribution (as $n \rightarrow \infty$) of the following:
$$ U_n = \frac{X_1 + X_2 + \ldots + X_n}{X_1^3 + X_2^3 + \ldots X_n^3},$$ where $X_i$ are iid $N(0,1)$.
2
votes
1answer
33 views
Proof of a PD covariance matrix for conditional Gaussian
I was looking at the formula for the conditional covariance of a partitioned matrix. I understand the intuition behind the equation for the conditional covariance, but I'm not sure how to show that ...
1
vote
1answer
78 views
How to show that $E[(\hat\theta -\theta)^2]<Var(\bar X)=\dfrac{1}{n}$?
Suppose $X_1, X_2, \dots, X_n$ are i.i.d $N(\theta, 1),\theta_0 \le \theta \le \theta_1$, where $\theta_0 \lt \theta_1$ are two specified numbers. Find the MLE of $\theta$ and show that it is ...
2
votes
2answers
67 views
Are the sample range and sample variance independent when population is normally distributed?
If a population is normally distributed, the sample mean and sample variance are independent.
What about the sample range and sample variance? Are they independent too?
I am trying to derive ...
0
votes
0answers
67 views
Transform non-normal data to normality by rescoring columns
I have a vector with fluency of translation - (0, 0, 1, 3, 3, 3 ,3 ....)
The problem is that it is made by people (for example someone gives too much 3 but only a bit of 2) and we want to normalize ...
1
vote
2answers
92 views
Function with variable having gaussian distribution
If I have a variable $X$ whose Gaussian distribution is known and let $f$ be a known function, is there a way to compute $f(X)$ i.e. the resulting Gaussian distribution from this? Is the result ...
0
votes
0answers
16 views
Evidential reasoning in Gaussian Bayesian Networks
I am working on Gaussian Bayesian Networks (GBN) i.e. the Bayesian Networks where all the random variables are continuous in nature. I am seriously trapped in the problem of evidential reasoning in ...
0
votes
1answer
56 views
Given known bivariate normal means and variances, update correlation estimate, $P(\rho)$, with new data?
I'm dealing with two correlated random variables which are modeled via a bivariate normal distribution. I have values for the means ($\mu_x, \mu_y$) and individual variances ($\sigma_x, \sigma_y$) of ...
2
votes
0answers
50 views
Mahalanobis distance for a multivariate normal distribution before and after uncorrelation
I have two questions:
Suppose we uncorrelate variables of a multivariate normal distribution using Cholesky transformation. Then:
What is the relation between Mahalanobis distances before and after ...
0
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0answers
36 views
Find the moment generating function
Find the moment generating function of $W$, when $W=X+2Y+4Z$. $~X,~Y,~Z$ are independent normal distributions $\mathcal N(1,4),~ \mathcal N(2,9) \text{ and }\mathcal N(3,16)$.
4
votes
0answers
37 views
How do I identify the “Long Tail” portion of my distribution?
I have a number of series that would typically be described as normal skewed or Gamma distributed. For example, say I have a group of customers and have calculated their spend over a fixed length of ...
2
votes
1answer
90 views
Asymptotic probability concerning the largest absolute value in an iid Gaussian sample
Let $v[n]$ be a vector $N$ $iid$ gaussian samples, of ~$N(0,\sigma^2)$ Also, let $v_{max}$ denote the maximum absolute value of all the samples given. (That is, if I took the absolute value of all the ...
0
votes
0answers
31 views
Difference of two gaussians [closed]
I got trouble understanding the following equation from a paper I'm currently studying [1]:
$\pi_{ij} \equiv \int^{\infty}_0 \mathcal{N}(s|\bar{s}_i - \bar{s}_j,2\sigma_s^2) ds$
...
1
vote
1answer
53 views
Using continuity correction for normal approximation or not?
Below is a question on a recent actuarial exam, Exam 3L of the CAS. I didn't know whether or not to use the continuity correction when using the normal approximation to do hypothesis testing ...
0
votes
1answer
68 views
How do I approximate the variance of a normal distribution?
I am approximating a 1D normal distribution by performing many samples. I can approximate its mean by simply averaging out the samples.
However, how do I get the variance? This doesn't seem so ...
0
votes
2answers
62 views
Simple homework question about normally distributed variables
The question states:
Consider a set of random variables $X_i$, where $i=1,...n$. Each $X_i$ is
normally distributed with mean $0$ and variance $1$, i.e. $X_i$ are $\mathcal N(0,1)$.
What is ...
1
vote
2answers
71 views
Pre-truncation moments for truncated multivariate normal
Suppose the random variable $Y$ has a multivariate normal (MVN) distribution, and consider truncating $Y$ in some way to create $T$. Given $T$'s mean and covariance matrix, I'd like to obtain $Y$'s ...
0
votes
0answers
25 views
marginal of the bivariate normal wrt correlation
What is the distribution that results by marginalizing the correlation coefficient of the bivariate normal distribution, assuming a uniform prior in angular space:
$$\int \; p(x,y|\mu,\Sigma(\theta)) ...
1
vote
1answer
39 views
Bivariate normal expectation of the sinus cardinal
I would like to get an analytical expression for
$$\mathbb{E}\left(\frac{\sin(aX)}{aX}\frac{\sin(bY)}{bY}\right)$$
or at least an analytical approximation thereof, when $a,b$ are positive reals, and
...
1
vote
1answer
62 views
Fast way to calculate difference in normal CDFs
I'm running a computationally intensive method where I have to calculate the difference in Normal CDF's millions of times, such as
pnorm(y)-pnorm(x)
I have not ...
0
votes
0answers
34 views
EM algorithms - confidence interval estimation
Does anybody know how to find the confidence intervals for estimated parameters of a mixture of Gaussians by using EM algorithm?
1
vote
2answers
80 views
Formula to calculate a t-distribution
I am writing an application that will be dealing with <30 observations in a normal distribution. My understanding is that this point I would need to use t-distribution. The thing is, this is easy ...
1
vote
1answer
34 views
How to correctly model noise?
Assume a linear mixing model $x = As$, where $x = (x_{0}, ..., x_{n})^T$ are linear mixtures of $s = (s_{0}, ..., s_{n})^T$, and $A$ is the mixing matrix.
Now, if I introduce additive noise to this ...
1
vote
1answer
36 views
how to calculate E[vech(x x')vech(x x')']?
Supposing a vector x follows normal distribution. I want to calculate the expectation of the "fourth moment" in a vector form, meaning $\text{E}[\text{vech}(x x')\text{vech}(x x')']$, given that we ...
3
votes
1answer
66 views
Expected value and variance of log(a)
I have a random variable $X(a) = \log(a)$ where a is normal distributed $\mathcal N(\mu,\sigma^2)$. What can I say about $E(X)$ and $Var(X)$? An approximation would be helpful too.
3
votes
1answer
60 views
Compute sum of vectors drawn from multivariate normal, subject to a linear constraint
I want to compute $S = \sum_{i=1}^n x_i$ where $w^t x_i>-1, \; \forall i$ and $x_i \tilde{} \mathcal{N}(\mu, \Sigma)$ for known $w$, $\mu$ and $\Sigma$.
I know $S$ can be approximated by sampling ...
0
votes
0answers
25 views
Probability that a given Normal Distribution is Maximum among others [duplicate]
You are given the mean and standard deviations of N normal distributions x1,x2...xn
What is the probability that x1 is maximum?
ie. Find P(x1>x2,x3..xn)
How do I go about solving this?
x1,x2,x3 etc ...
0
votes
1answer
31 views
How to get the diagonal elements of a covariance matrix from its sparse precision matrix
I have a equation to solve Ax = b, where A happes to be the precision matrix of a multivariate gaussian distribution. I can use either direct solver or iterative solvers to get the x vector. However, ...
1
vote
1answer
35 views
Reshaping a distribution
Not sure what the exact term is for what I'm trying to do.
I have a data set with random variable x with values X1, X2, ..., XN that has a standard deviation sigma and a mean m.
I want to perturb ...
0
votes
0answers
34 views
Is a multivariate normal restricted to an affine set normal? [duplicate]
This seems like a basic question, but I've been confused about it anyway.
Let $X$ be a multivariate normal random variable in $\mathbb R^n$. Let $A$ be the affine set $\{x\in\mathbb R^n : ...
2
votes
2answers
31 views
Convergence of empirical distribution parameters of a sequence of generated normal variables
I am generating a sequence of normal random variables (using the routines from boost C++ library). How fast would you expect the mean and the variance of the sequence converge to the actual variance?
...
1
vote
1answer
43 views
Truncated Normal — Reproduce a randomly generated data set
help.
Problem:
Given a bounded Gaussian Distribution -- looking reproduce similar results i.e. same mean and standard deviation randomly.
Definition:
Data set exhibits properties of a Gaussian ...
1
vote
1answer
50 views
Use the Central Limit Theorem to calculate the approx probabilities of Gamma RVs?
If $X_i, i=1,...,$ are independent, identically distributed $\operatorname{N}(0,1)$ random variables, and $Y_i = X_i^2$ are independent $\operatorname{Gamma}(\frac{1}{2},\frac{1}{2})$ RVs, use the ...
1
vote
0answers
36 views
Transforming data: correlate regardless of distribution
Is there a way to correlate data regardless of distribution? I know the Choleksy transformation is used for normally distributed data, but is there a general method that applies to any case?
To ...
1
vote
2answers
73 views
Is it possible to use a two sample $t$ test here?
I want to do statistical analysis to compare the results of the different specimen sizes (which I am comparing) with each other. Seeing as I have at least 12 specimens for each specimen size, I ...
1
vote
0answers
76 views
subtraction of two multivariate normal distribution
Assume that we have a $n$-dimensional vector that shows the position of a point and two multivariate normal distributions with means $\mu_1$ and $\mu_2$, and covariances $cov_1$ and $cov_2$.
I’m ...
4
votes
3answers
214 views
How to test my data against an specific normal distribution?
I need to test my data to see if it follows a normal distribution with specific mean and std like N~(mu, std) I know that this can be done by Kolmogorov-Smirnov test which has a function in both ...
