Tagged Questions
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. ...
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 $N(0,1)$.
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 ...
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
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 ...
2
votes
1answer
67 views
The sample size applied to a non-normal distribution
I have a single variable that represents my population values (sample of data):
...
0
votes
0answers
42 views
Determining sample size in a non-normaly distributed data
I want to take some samples from a database nearly ~150.000 records of a non-normally distributed values. From this link I obtained some common procedures to find a sample, influenced by The level of ...
5
votes
3answers
231 views
Generate distribution based on descriptive statistics
There's a hidden variable that I'd like to approximate. I know several summary statistics: min, max, mean, median, standard deviation, n; and that it's approximately normal.
I can obviously do a ...
1
vote
1answer
48 views
Proof of distribution $\chi_n ^2$?
I have the problem of proofing that
$$X=(1/\sigma^2) \sum_{i=1}^{n} Y_i ^2$$
where $Y_i \sim N(0,\sigma^2)$ is $\chi_n ^2$ distributed with $E(X)=n$:
My proof that $E(X)=n$:
$$E(X)=E((1/\sigma^2) ...
0
votes
2answers
69 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
82 views
Fitting t distribtution to financial data
The data I am using can be found here: http://uploadeasy.net/upload/nwv0.rar
The variable is called "alvsloss".
I want to fit a distribution to my financial data. First of all, I started with a ...
-3
votes
1answer
70 views
The distribution of Gaussian density at a fixed point given random mean
Let's say I have random variable $\mu \sim N(\mu ; 0, \xi^2)$. Is there anything useful known about the distribution of random variable $d = N(x ; \mu, \sigma^2)$, that is, the distribution of density ...
1
vote
1answer
102 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 ...
1
vote
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
...
1
vote
0answers
151 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 ...
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 ...
4
votes
0answers
67 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 = ...
5
votes
2answers
161 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
101 views
Bayesian updating - which distribution to use
I'd like to use Bayesian updating to form price expectations to be used in another model. I'm very new to this area, so your help would be highly appreciated.
I'm not sure which distribution to use ...
0
votes
0answers
65 views
Working with an arbitrary number of sample moments
The $n^{th}$ moment of a distribution can be estimated from a vector of samples $(x_1,x_2,...x_k)$ by:
$$
\sum_{i=1}^{k} x_i^n
$$
Now, let's say I've calculated the first $m$ moments for my ...
6
votes
1answer
96 views
Generalization of multivariate normal distribution and classification
I am interested in a family of multivariate distributions that can be seen as a generalization of the multivariate normal distribution, insofar as they are defined by an expectation value $\vec \mu$ ...
4
votes
1answer
163 views
Inequality for bivariate normal distribution
Let $X_1$ and $X_2$ be bivariate normal with mean $\mu=(0,\mu_2)$, for any $\mu_2$, and correlation $\rho$.
Consider the following inequality:
\begin{align*}
Pr\left\{|X_1| \ge ...
3
votes
1answer
173 views
Order statistics of absolute value of bivariate normal distribution
Suppose $X_1$ and $X_2$ are bivariate normal and let $|X|_{(1)}$ and $|X|_{(2)}$
be the ordered version of their absolute value. I am interesting in finding the following probabilities or some bounds ...
0
votes
0answers
205 views
Descriptive statistics for non normal data
When I use an histogram to plot my data in Stata almost all variables cluster around one value, i.e. these are either at 0 or 1 (a huge bar at one or 0). What does it show and how should I correct it? ...
5
votes
5answers
776 views
How to determine whether data is slightly or extremely non-normally distributed?
I'm a PhD student and doing a research on regression analysis.
My question is how to determine whether the data is slightly, moderately or extremely non-normally distributed?
4
votes
1answer
138 views
What are the connections between: the normal, the $\chi^2$ & the F distributions?
I have often read that there is a huge connection between the normal distribution and several other distributions. But these were only mathematical explanations.
What's the "real" connection between ...
2
votes
0answers
99 views
Continued fraction representation of the multivariate normal distribution [closed]
Can anybody help me with a continued fraction representation of the multivariate normal distribution? Such a representation is well-known for the univariate case; see, for example,
C-I. C. Lee. On ...
2
votes
0answers
84 views
Is there a name for distributions induced by norms?
The log density of a multivariate Gaussian is proportional to $||x-\mu||_2^2$, i.e. the norm of the difference between $x$, the random variable, and $\mu$, the mean of the distribution (assuming a ...
5
votes
3answers
240 views
Is there any test for a null hypothesis of non-normality?
I'm currently looking for a test having for null hypothesis that the sample does not come from observing a normally distributed random variable. In other words, I'd like to know if there's a test ...
8
votes
0answers
259 views
Gaussian Ratio Distribution: Derivatives wrt underlying $\mu$'s and $\sigma^2$s
I'm working with two independent normal distributions $X$ and $Y$, with means $\mu_x$ and $\mu_y$ and variances $\sigma^2_x$ and $\sigma^2_y$.
I'm interested in the distribution of their ratio ...
6
votes
2answers
1k views
How is Poisson distribution different to normal distribution?
I have generated a vector which has a Poisson distribution, as follows:
x = rpois(1000,10)
If I make a histogram using ...
4
votes
4answers
1k views
What are the standard statistical tests to see if data follows exponential or normal distributions?
What are the standard statistical tests to see if data follows exponential or normal distributions?
6
votes
2answers
255 views
Probability density function between -1 and 1?
I'm currently using Gaussian distribution as a mutation operator for my genetic algorithm. However, I only want to obtain values between -1 and 1. I also don't wish to truncate my Gaussian ...
6
votes
2answers
180 views
Estimating the parameters of a sum of a Gaussian and an $\alpha$-stable random variable
Let's assume I have a set of samples of a random variable
$$
X = Y + Z \>,
$$
where $Y$ is Gaussian (with a mean of zero and variance $\sigma^2$) and $Z$ has a symmetric $\alpha$-stable ...
6
votes
3answers
232 views
What distribution can be closely (or precisely) fit to the “5 number summary” statistics?
I'm programming a web tool (="I'm a stats ignoramous who drifted here from stackoverflow.com") that allows scientists to enter predictions about the 5-number-summary stats for a variable. Entry is ...
2
votes
1answer
242 views
What happens if you reject normality of residuals when estimating with least square ?
What happens if you reject normality of residuals when estimating with least square ?
Is it too important to have normality on the residuals?
1
vote
0answers
339 views
Can two dependent rvs X and Y that are nonnegative have a normal distribution for X-Y? Can it be done with half normals?
A question was asked whether or not two independent variables $X$ and $Y$ that take on only positive values can have $X-Y$ be a normal distribution. I was shown that the answer is no. But I think ...
0
votes
1answer
57 views
Conditional on Gaussian, need clarification
I'm reading Andrew Ng's notes on machine learning, and on page 12 of this document, he makes a step in his proof that I'm trying to decipher:
Let $\textbf{x} = \left( 1 , x_1 , x_2 , \cdots , x_n ...
4
votes
2answers
462 views
Mean and variance of log-binomial distribution
If X is a random variable with a normal distribution, then Y = exp(X) has a log-normal distribution.
Likewise if X is a random variable with a binomial distribution, then Y = exp(X) has a ...
1
vote
1answer
864 views
How can I calculate cut-off points from a normal distribution?
I'm trying to calculate the upper percentage points for the 0.99 percentile for samples drawn from a normal distribution, with a sample size of 500. How can I calculate the expected values for ...
2
votes
1answer
274 views
Does a stationary process implies a normal distribution of the data?
My understanding is 'no', a stationary process does not imply a normal distribution of the data. However I haven't found a clear indication in my library or online. I am interested in other resources ...
4
votes
1answer
149 views
Distribution of random effects
Why do we usually assume that random effects come from a normal distribution? Can we assume another distribution? Or maybe because the CLT indicates that a random effect is normally distributed?
6
votes
2answers
697 views
How can I check whether two signals are jointly normally distributed?
As explained on this Wikipedia page, if two random variables X and Y are uncorrelated and jointly normally distributed, then they are statistically independent.
I know how to check whether X and Y ...
6
votes
1answer
355 views
How can I prove the experiment data follows heavy-tail distribution?
I have several test results of server response delay. According to our theory analysis, the delay distribution (The probability distribution function of response delay) should have heavy-tail ...
3
votes
2answers
192 views
Adjusting for tilt of the earth
I have rewritten the old question (below) to hopefully make things a bit clearer.
Basically I think that the temperature of the earth should be normally distributed but is not due to the ‘seasonal ...
1
vote
1answer
386 views
What is a normal distribution with 'common variance'?
Data Augmentation Approach in Bayesian Modelling of Presence-only Data (Divino et al.) states that the data ware sampled from a normal distribution with mean 2.0 and a common variance (section 3). ...
0
votes
2answers
409 views
How to demonstrate failure of CLT in R?
I was assigned to demonstrate the Central Limit Theorem (CLT) in R in my statistics class. I already made some progress with simulation using simple.sim in R. I want to prepare 3 examples of the CLT ...
3
votes
2answers
240 views
Density of a quadratic transformation of a normal random variable
Consider the normally distributed random vector
$$X \sim \mathcal{N}(\mu, \Sigma)$$
What is the distribution of $Y = f(X)$?
For general $f$ this is a challenging problem but for the affine linear ...
2
votes
1answer
805 views
How to test homogeneity of variance if the data may not be normally distributed?
I need a test to check for homogeneity of variances. I am not sure if a series is normally distributed.
If I use a test of homogeneity of variance that works for NON-normally distributed data, does ...
3
votes
1answer
257 views
Higher order generalization of the multivariate normal distribution
In some sense the multivariate normal is the "nicest" distribution that we can describe using only a vector (rank one tensor) and a symmetric positive definite matrix (rank two tensor).
...
