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 ...
4
votes
1answer
69 views
Given samples from multiple normal RVs, how do we recover the histogram of their means?
Let $X_1,...,X_N$ be independent normal random variables. $X_i$ is normal with mean $\mu_i$ and standard deviation $\sigma_i$. Let $x_i$ be a single random sample from $X_i$.
Input: We get all ...
0
votes
0answers
8 views
Issues with estimating the sparse inverse covariance matrix with Glasso
I am trying to estimate the sparse inverse covariance matrix of my gaussian graphical model. I installed the glasso package in R and tried out some examples.
After that I ran the glasso software on ...
0
votes
0answers
14 views
Properties of bivariate standard normal and implied conditional probability in the Roy model
Sorry for the long title, but my problem is quite specific and hard to explain in one title.
I am currently learning about the Roy Model (treatment effect analysis).
There is one derivation step at ...
1
vote
1answer
51 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
0answers
6 views
Confusion related to dual problem formulation in sparse inverse covariance matrix estimation
I was reading this paper where they are trying to estimate the inverse covariance matrix of the gaussian. What they are trying to maximize the gaussian log likelihood. The primal problem is maximize ...
0
votes
0answers
19 views
Problem with the formulation of a gaussian copula likelihood function
I recently got to hear about copulas which to me sounded like a nice tool to model relationships between variables. I decided to try to implement the likelihood function for a bivariate Gaussian ...
1
vote
1answer
46 views
Is it appropriate to use SE in place of SD in rnorm()?
I have wood density data for a number of tree species given a tree's state of decay. I am presented with mean density and standard errors (SE). I am NOT provided with sample sizes.
For example, a ...
0
votes
1answer
28 views
How do I use a mean and 95% confidence intervals to draw from a distribution? [duplicate]
I have a number of parameters for a model. The parameter values are presented as the mean and the 95% confidence interval. I am not provided with standard deviation or sample size.
I am using R. I ...
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 ...
1
vote
0answers
31 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
votes
0answers
78 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
39 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 ...
4
votes
1answer
82 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 ...
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
43 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 ...
2
votes
1answer
188 views
Obtaining the covariance matrix of a Gaussian random vector
I'm looking for some advice about a problem I've been assigned to solve. This is the problem. Suppose a car has to travel from P1 to P4, with intermediate points P2, P3. Say $X1$ is a r.v. that ...
0
votes
0answers
55 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 ...
0
votes
0answers
31 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
101 views
How can I test the difference between a population proportion and sample proportion?
A report says that 82% of British Columbians over the age of $25$ are high school graduates. A survey of randomly selected residents of a certain city included $1290$ who were over the age of $25$, ...
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
45 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 ...
1
vote
2answers
93 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 ...
1
vote
4answers
2k views
Generating a Gaussian dataset in MATLAB
I want to generate a bivariate Gaussian dataset. The dataset includes a total of 800 results drawn randomly from four two-dimensional Gaussian classes with means $(-3,0)'$, $(0,0)'$, ...
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 $N(0,1)$.
6
votes
2answers
436 views
How to differentiate two subgroups from a histogram?
I have a set of samples in which I assume there are 2 definite subsets in it. I plotted their values in a histogram and found that there are two distinct modes as shown in the figure below.
My ...
0
votes
1answer
62 views
Parameter estimation with GMM
I have estimated the parameters of normal distribution with GMM
and got the follwing results :
mean = -0.01168 , p-value = 0.83519
i'm bit confused in interpreting the result. can i say that the ...
2
votes
1answer
34 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 ...
2
votes
2answers
68 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 ...
1
vote
1answer
80 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 ...
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
78 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 ...
5
votes
2answers
944 views
How to compute an accuracy measure based on RMSE? Is my large dataset normally distributed?
I have several datasets on the order of thousands of points. The values in each dataset are X,Y,Z referring to a coordinate in space. The Z-value represents a difference in elevation at coordinate ...
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
votes
0answers
37 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 $\mathcal N(1,4),~ \mathcal N(2,9) \text{ and }\mathcal N(3,16)$.
2
votes
1answer
91 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 ...
4
votes
0answers
38 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 ...
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 ...
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
56 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
70 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
1answer
109 views
Metropolis-Hastings algorithm, using a proposal distribution other than a Gaussian in Matlab
I am currently working on my final year project for my mathematics degree which is based on giving an overview of the Metropolis-Hastings algorithm and some numerical examples. So far I have got some ...
1
vote
2answers
2k views
Correlation between dichotomous and continuous variable
I am trying to find the correlation between a dichotomous and a continuous variable.
From my ground work on this I found that I have to use independent t-test and the precondition for it is that the ...
0
votes
2answers
70 views
Normal approximation to binomial
What do I do when the normal approximation is not valid?
Here's the question I'm trying to answer:
A student guesses all 15 answers on a multiple-choice test. There are 5 choices for each of the ...
1
vote
1answer
40 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
...
0
votes
1answer
40 views
Questions about the sampling distribution of the sample mean
(a) Let $X_1,X_2,\cdots,X_n$ be a random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$.
Show that
$E[\bar{X}]=\mu$ and $V[\bar{X}]=\frac{\sigma^2}{n}$
What is the ...
0
votes
1answer
150 views
WinBUGS truncated normal distribution
I am estimating a stochastic frontier with a mixed model.
So far the half normal distribution worked good but I need a truncated normal distribution. It does not work, and I receive the error ...
