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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1answer
231 views
Finding the z score and p-value of a binomial distribution
Emily is a big fan of lady gaga, and 20% of the songs on her ipod are lady gaga songs. Suppose Emily has her ipod on shuffle and repeat mode, which can be assumed to mean that each song to be played ...
0
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2answers
109 views
Why doesn't this represent a normal approximation to the binomial?
Suppose the registrar's office at a college reports 58% of the students live on campus. An intern working in the administration building is unaware of this 58% parameter value. He designs a study in ...
2
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1answer
311 views
probability of one random variable being greater than another
Using the normal distribution. Let $X \sim N(1, 2)$ and $Y \sim N(2, 3)$ where $N(\mu, \sigma^2)$ denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. $X$ and $Y$ are independent.
...
1
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0answers
69 views
Do we normalize too much? [closed]
Yesterday i read this blog post Predictors, responses and residuals: What really needs to be normally distributed?
and I wonder what do you think about it. Personally I totally agree with the ...
1
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1answer
55 views
Approximate distribution of normal squared
I am studying for a test, one section of which will cover the delta method. This problem came from that section:
Let $X\sim N(\mu,n^{-1})$. Find an approximate distribution of $X^2$. (It also asks ...
3
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1answer
98 views
Estimating parameters of a normal distribution from noisy observation of samples
Suppose I have a number of samples drawn from a normal distribution $x_i \sim \mathcal{N}(\mu,C)$ with $i = 1 \dots n$. I can make observations $z_i = x_i + e_i$ for those samples which are perturbed ...
1
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0answers
47 views
Plotting a histogram estimate together with an analytical solution of the mean and covariance parameters
How do I plot a histogram estimate of this marginal distribution p(x1):
...
2
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2answers
70 views
0
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1answer
99 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 $25$, ...
0
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1answer
87 views
Spherical Gaussian Sigma dimension
I think I am confused with this thing.
If we have a 3 dimension Gaussian then the MLE estimate for $\mu$ is a vector with 3 element
$$\mu(1)' = \frac{1}{n}\sum_{j = 1} ^ n x_j\text{ and so on ...
1
vote
1answer
101 views
Distribution which has maximum or minimum variance for a given entropy
We know that the normal distribution has the maximum entropy among all continuous distribution on $\mathbb{R}$ for a given variance.
I wonder what's the opposite, i.e. what distribution has the ...
2
votes
1answer
104 views
Standard deviation of a particular dimension in a multivariate Gaussian distribution
I have a set (cluster) of vectors in dimension d. From this I have calculated the sample mean and covariance matrix ( I make the assumption that they are from a multivariate Gaussian).
My question ...
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 ...
0
votes
0answers
61 views
combine two Normal Dists, with one the mean of the other
For an assignment, I need to find $E_{y|\theta} [- \frac{\partial^2}{\partial^2\theta} \ln[P(y|\theta)] ]$, where $y \sim \mathcal{N}(\theta, 1)$ and $\theta \sim \mathcal{N}(0, \delta^2)$.
I can ...
3
votes
1answer
92 views
How to Calculate a Z-Score from Power Log Distributions
Please forgive me if the question is non-sensical as I only have a elementary knowledge of statistics, and I have no idea where to start.
I want to perform an analysis of some web analytics ...
3
votes
1answer
87 views
covariance of RVs under a nonlinear transformation
I have a multivariately distributed random 3-vector
...
1
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1answer
43 views
Approximating binomial distribution by normal distribution
I got a very small probability in my homework so are there any mistakes?
Benford's law says that if we have a collection of numbers, the first digit has the distribution ...
0
votes
1answer
146 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 ...
8
votes
1answer
287 views
Central limit theorem and the law of large numbers
I have a very beginner's question regarding the Central Limit Theorem (CLT):
I am aware that the CLT states that a mean of i.i.d. random variables is approximately normal distributed (for $n \to ...
0
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0answers
147 views
repeated measurements study using JMP - how to make a difference plot when data is unbalanced
My study is a repeated measurement design where I'm going to show reproducibility of pulse wave velocity measurements on minipigs.
I have read a lot of articles about reproducibility, both veterinary ...
3
votes
1answer
227 views
Finding gaussian distribution given 15th and 50th percentile.
My knowledge of statistics are small so I need a little bit of help.
I have some data showing the relationship between age and walking speed. The numbers of walking speed are presented only as the ...
1
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0answers
48 views
Analyzing trends in distributions
I have around 9000 cases; per case and per year, I have a value ranging from 0 to 1 explaining the distribution of events (for exact context, see my other question)
Example data would look like this
...
5
votes
1answer
193 views
Normal distributed random numbers in time - expected behaviour - askew distributions?
I have a 3D array of numbers, initialised with normal distributed values. The mean of the distribution is $0$, the standard deviation in the order of $10^{-5}$ to $10^{-8}$, but would be constant for ...
7
votes
2answers
342 views
Estimating parameters of a normal distribution: median instead of mean?
The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance.
However, if there are some outliers, the median and the ...
0
votes
0answers
58 views
Constraints on ML for mixture of Gaussians
I have some data sampled from a mixture of two Gaussians where one of them is known, and the density function is as follows:
$f(x, \mu, \sigma) = \frac{1}{2}\frac{1}{\sqrt{2\pi}\sigma} ...
0
votes
1answer
71 views
Berry-Esseen theorem
In the Berry-Essen theorem, why is the standard normal distribution used in the context of the closedness of two distributions? Why can't we use the general normal distribution where will things will ...
0
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0answers
47 views
How to sample from a multivariate normal given the $P^T LDL^T P$ decomposition of $\Sigma$?
How to sample from a multivariate normal given the $P^TLDL^TP$ decomposition of $\Sigma$, and $\mu$?
Here, $P$ is a permutation matrix, $L$ is lower-triangular, and $D$ is diagonal
Given the ...
1
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0answers
58 views
Conjugate prior for a Gaussian model with shifted variance
Consider a set of observations $ \{ y_i \}$ and assume a Gaussian model for these data: $y_i \sim \mathcal{N}(\mu, \sigma^2)$. Suppose the mean parameter $\mu$ is known, but the variance parameter ...
0
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0answers
43 views
What does taking the logarithm of a variable mean? [duplicate]
Possible Duplicate:
When are Log scales appropriate?
Say you have a bar graph displaying data, for example, "Cost of Computer Orders by Population", and you are trying to analyze the data ...
1
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0answers
149 views
Transforming Percent Change: Lognormal Distribution?
I am dealing with a dependent variable relating to the price of an asset and the percent change in the price of that asset. The problem with this type of analysis, like when stocks are the unit of ...
-1
votes
2answers
105 views
are data sets obtained from a Normal distribution normal?
I have 10 vectors each having 100,000 points ( Muscle activity obtained by sampling at a rate of 10 Khz). I take integral of each data set to have 10 values. I want to know whether these 10 values are ...
3
votes
0answers
114 views
Correlated bivariate normal distribution: finding percentage of of data which is 2 standard deviations above the mean?
Background
Background: in an essay of mine, I point out that if a selection process (like higher education) requires successful applicants to be above the mean on 2 different variables, there will ...
-1
votes
1answer
198 views
Combined probability of multiple Gaussian experiments with differing observations [closed]
Observations of three independent Gaussian experiments have yielded probabilities of .1, .2 and .9. I'm trying to accept or reject a hypothesis that the results can be explained by Gaussian behavior. ...
0
votes
1answer
96 views
How to generate an orthogonal vector
I have two vectors $a$, $b$ each containing $10$ random numbers from the standard normal distributions. I want to generate another vector $C$ of $10$ numbers from the standard distribution where ...
1
vote
1answer
82 views
Computing conditional expectation of ordered normal random variables
There are $m$ normally distributed, independent random variables $N_1, \ldots, N_m$ with distinct means $\mu_1, \ldots \mu_m$ and standard deviations $\sigma_1, \ldots, \sigma_m$. Then, we observe a ...
2
votes
3answers
2k views
How does the sampling distribution of sample means approximate the population mean?
I am trying to learn statistics because I find that it is so prevalent that it prohibits me from learning somethings if I don't understand it properly. I am having trouble understanding this notion of ...
3
votes
2answers
206 views
Kriging on log transformed rainfall data
I am beginner in R. I had found in the literature that prior to performing kriging on the data, the distribution has to be investigated to check if it is Gaussian.
So, in order to check if the data ...
2
votes
1answer
136 views
How to simulate sum of two normal distributed variables when linearly transformed?
I m trying to replicate a paper's simulation results, but am not having much success. The equation is:
$$
P_t = \beta_{PD}*X_t + \varepsilon_{PD,t}
$$
$P_t$ (by assumption) is described as ...
7
votes
1answer
231 views
Finding the distribution of a statistic
Studying for a test. Couldn't answer this one.
Let $X_{1,i},X_{2,i},X_{3,i}, i=1,\ldots,n$ be iid $\mathcal{N}(0,1)$ random variables. Define
$W_i = (X_{1,i} + X_{2,i}X_{3,i})/\sqrt{1 + ...
0
votes
1answer
290 views
How do you calculate the derivative of the multivariate normal CDF with respect to a correlation coefficient?
How does one calculate the derivative of a multivariate normal CDF with respect to a given correlation coefficient?
I have started with the bivariate case but couldn't work it out.
4
votes
0answers
66 views
Transforming two normal random variables
I'm reviewing for a test, and I am not sure if I am getting the right solution.
Let $X$ and $Y$ be iid $\mathcal{N}(0, \sigma^2)$ random variables.
a. Find the distribution of $U = X^2 + Y^2$, $V = ...
3
votes
1answer
275 views
Maximum likelihood of function of the mean on a restricted parameter space
I've been trying to teach myself some of the fundamentals of statistics by trying to work through old qualifying exams. Here's a problem:
Suppose $X_1, \ldots, X_n$ are a random sample from a normal ...
3
votes
3answers
236 views
How to estimate the parameters of a Gaussian distribution sample with outliers?
I have a sample of length $N$, mostly taken from a Gaussian distribution with unknown mean and variance. Of those $N$ samples, some proportion of them (typically less than 1-2%) are outliers, taken ...
0
votes
1answer
70 views
Can I use RM ANOVA instead of Friedman
I am currently analysing my quantitative data. My sample size is 157 students who sat for a survey in 2 phases after an intervention. The same students sat for the same survey on positive outcomes on ...
2
votes
1answer
112 views
Confusion related to derivation of the log likelihood
I was reading the Hastie, Friedman, Tibshirani paper "Sparse Inverse Covariance Estimation with the Graphical Lasso" and it had the following
I couldn't get how the following expression was derived
...
0
votes
0answers
104 views
Sampling from a multivariate normal distribution
When we sample $n$ things from a multivariate normal distribution $N(\mathbf{\mu}, \mathbf{\Sigma})$, does this mean that we choose $n$ vectors of some fixed length $k$? For example, suppose $n=3$ and ...
1
vote
1answer
41 views
Confusion related to derivation of product of gaussian
I am confused. Given
how come this is derived?enter image description here
5
votes
2answers
160 views
Distribution of ratio of sample means from two independent normal variables?
The Question
We have a sample of size $N$ with mean $\bar{x}$ and SD $\bar{\sigma_x}$ from a random variable $X \sim \mathcal{N} (\mu, \sigma^2)$
We have a sample of size $M$ with mean $\bar{y}$ and ...
1
vote
1answer
78 views
Flying Bomber aircraft through SAM sites - combining normal distributions
I have been puzzling over this for days but I don't think this was covered at school
We simultaneously fly a known number of bomber aircraft, K, through three sequential batteries of surface to air ...
0
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0answers
66 views
Thompson sampling with multivariate posterior distribution
I'm implementing Thompson sampling for a multi armed bandit problem (see http://en.wikipedia.org/wiki/Thompson_sampling). The underlying Bayesian model is a Bayesian Linear Regression, which has a ...
