All Questions
4,885 questions
2
votes
1
answer
663
views
How to understand if the variance is constant reading GARCH model output?
I'm using GARCH() function (tseries package) to fit garch model.
I tried it with random numbers: ...
- 2,697
1
vote
2
answers
1k
views
Need an example of RV with a mean and no second moment
An example like the t-distribution with 2 degrees of freedom would not suffice as the second moment exists but equals inf.
15
votes
1
answer
18k
views
Mean and variance of a zero-inflated Poisson distribution
Can anyone show how the expected value and variance of the zero inflated Poisson, with probability mass function
$$
f(y) =
\begin{cases}
\pi+(1-\pi)e^{-\lambda}, & \text{if }y=0 \\
(1-\pi)\frac{\...
- 8,850
20
votes
3
answers
19k
views
Maximum value of coefficient of variation for bounded data set
In the discussion following a recent question about whether the standard deviation can exceed the mean, one question was raised briefly but never fully answered. So I am asking it here.
Consider a ...
- 47.8k
73
votes
4
answers
191k
views
How do you calculate the probability density function of the maximum of a sample of IID uniform random variables?
Given the random variable
$$Y = \max(X_1, X_2, \ldots, X_n)$$
where $X_i$ are IID uniform variables, how do I calculate the PDF of $Y$?
- 871
5
votes
1
answer
630
views
How can I compare two classifications?
My job is to develop a classification that groups together diagnoses of similar cost and procedures of similar cost, by similar anatomy. For instance a hip replacement would not be in the same group ...
6
votes
4
answers
9k
views
What is the difference between test to check homogenity of variance and ANOVA?
I found many tests like: Fligner, Levene etc etc to check homogeneity of variances, my question is: What is the difference between those tests and ANOVA ?
- 2,697
290
votes
11
answers
170k
views
How would you explain covariance to someone who understands only the mean?
...assuming that I'm able to augment their knowledge about variance in an intuitive fashion ( Understanding "variance" intuitively ) or by saying: It's the average distance of the data ...
- 14.9k
5
votes
1
answer
1k
views
Is there a method to check the homogeneity of variance of a single time series?
I have a data frame with prices/dates, is there a method that checks if the variance is homogeneous during all the series? I know there are many test like fligner.test, bartlett.test but I need to ...
- 2,697
2
votes
0
answers
67
views
Looking for formalization of the idea of low-variance predictors
In baseball, Bill James suggested using, to predict next season's winning percentage
runs_scored^2/(runs_scored^2 + runs_allowed^2), rather than this season's ...
- 191
2
votes
1
answer
1k
views
How to deal with a non-gaussian distribution & heteroscedasticity
I am working on my thesis project and have come across a problem with the statistics which I am looking for a bit of guidance.
I am running ANOVA tests to determine significance between groups but
i ...
- 21
60
votes
5
answers
228k
views
What is the difference between N and N-1 in calculating population variance?
I did not get the why there are N and N-1 while calculating population variance. When we use ...
- 984
7
votes
1
answer
519
views
How does number of observations supporting alternate hypothesis on a test of a variance have to scale so that null is rejected?
Informal explanation: In the course of my research I've run into the following problem: I am observing a machine that outputs random numbers. Most (if not all) of these random numbers come from the ...
- 1,079
110
votes
13
answers
74k
views
Understanding "variance" intuitively
What is the cleanest, easiest way to explain someone the concept of variance? What does it intuitively mean? If one is to explain this to their child how would one go about it?
It's a concept that I ...
- 14.9k
7
votes
1
answer
1k
views
Is my data distribution normal? (Tried Shapiro and Kolmogornov-Smirnov tests)
I have a 1D data set with 83163 data points, and I would like to know whether the data follows a normal distribution.
I tried using shapiro.test and ks.test in R:
d is a vector containing the data
...
- 281
13
votes
2
answers
1k
views
Parametric modelling of variance of count data
I am looking to model some data, but I am not sure what type of model I can use. I have count data, and I want a model that will give parametric estimates of both the mean and the variance of the ...
- 1,081
12
votes
3
answers
5k
views
Is there a reference that legitimises the use of the unpooled z-test to compare two proportions?
The z-test to compare two proportions is $\newcommand{\p}{\hat{p}}\newcommand{\v}{\mathrm{Var}} z=\frac{\p_1-\p_2}{\sqrt{\v(\p_1-\p_2)}}$. Usually it is defined that
$$\v(\p_1-\p_2)=\p(1-\hat{p})(1/...
- 1,100
10
votes
2
answers
11k
views
How to find when a graph reaches a peak and plateaus?
This may sound very basic, but I have this problem:
I've got a queue of data with a window size of 300. New data is added at one end, old values are removed from the other end.
I expect the queue ...
- 203
7
votes
1
answer
8k
views
Comparing standard deviations between variables with very different ranges
I have a number of variables for which I want to compare the standard deviations. Each of these variables is actually the data for a particular wavelength of light, and I want to produce a plot ...
- 2,177
20
votes
2
answers
54k
views
What is the difference between sample variance and sampling variance?
What is the difference between sample variance and sampling variance? They seem same. Aren't they?
- 984
2
votes
1
answer
4k
views
How can I calculate proportion of variance of an aggregate time-series accounted for by the variance of a sub-series?
How can I calculate proportion of variance of an aggregate time-series accounted for by the variance of a sub-series? As I'm not sure what the correct terminology is for explaining my question, I'll ...
- 4,997
2
votes
1
answer
4k
views
Bound on variance of sum of variables
Suppose I have two finite sets of data A and B, with equal length n.
What's the best upper ...
- 267
5
votes
1
answer
237
views
How is it possible that these variances are equal?
I'm using the Fligner-Killen test to analyze the residuals of a linear regression.
I subdivide those residuals in three groups and then I do the FK test to check the homogeneity of variances.
The ...
- 2,697
3
votes
2
answers
2k
views
How to test the variance in timeseries?
I have a doubt regarding the variance, I try to explain It with an example.
I have two vectors, like:
...
- 2,697
2
votes
1
answer
185
views
How to understand if the points are constant around a line?
I would like to understand how can I check if some points around a line have constant distance between the point and the line.
So image a normal chart(cartesian plane) with a line that is formed with ...
- 2,697
1
vote
1
answer
690
views
Slope and intercept of linear equation of uniformly distributed variables
Consider the random variable $y_M$ which equals the sum of $M$ independently uniformly distributed random variables; i.e., $y_M = x_1 + x_2 +\ldots + x_M$, with the assumption that each of the $x_i$ ...
- 147
43
votes
2
answers
75k
views
Variance of product of dependent variables
What is the formula for variance of product of dependent variables?
In the case of independent variables the formula is simple:
$$ \operatorname{var}(XY) = E(X^2Y^2) - E(XY)^2 = \operatorname{var}(X) \...
- 133
19
votes
2
answers
12k
views
What is the variance of the maximum of a sample?
I'm looking for bounds on the variance of the maximum of a set of random variables. In other words, I'm looking for closed-form formulas for $B$, such that
$$
\mbox{Var}(\max_i X_i) \leq B \enspace,
$$...
- 273
2
votes
0
answers
552
views
How to create a ratio distribution from samples?
Ok, let's try again. The context of the original question is given below, but perhaps it helps to focus on the statistical aspect to get an answer.
What I got is a number of measurements in unit t. ...
- 121
1
vote
1
answer
1k
views
Mean and variance of a normally distributed random number created from the average of a set of uniformly distributed random numbers
An old-fashioned way of generating normally distributed random numbers entailed setting each normally distributed random number equal to the average of a set of uniformly distributed random numbers, ...
- 147
17
votes
3
answers
165k
views
How to use Levene test function in R?
I'm a newbie to statistics and R and I have a trouble with using Levene function (I would like to check the equality of variance of two samples).
The documentation says that I should run:
levene....
- 737
3
votes
0
answers
277
views
Confidence of a variance estimate [duplicate]
Possible Duplicate:
Calculating required sample size, precision of variance estimate?
I would like to present some measure of how variable a particular phenomenon is. This phenomenon appears to ...
- 3,191
1
vote
0
answers
521
views
Variance of coefficients in nonlinear regression
I was reading the short intro to nonlinear regression in R by John Fox (Link)
and was wondering where the formula for the variance of the coefficients come from (page 1). The formula for the variance-...
- 8,850
3
votes
1
answer
2k
views
Why does a paired t-test (when appropriate) result in better variance?
I didn't quite get the Wikipedia explanation here:
http://en.wikipedia.org/wiki/Paired_difference_test#Use_in_reducing_variance
I agree that both the unpaired and paired means are the same...then I ...
- 1,003
6
votes
2
answers
3k
views
Putting a confidence interval on the mean of a very rare event
I'm simulating an extremely rare event (the detection of weighted photon packets in a highly absorbing material). For example, I may simulate the transmission of 1e9 photons and only detect 10 of them ...
- 373
2
votes
1
answer
3k
views
Why the Breusch-Pagan test fails if I set the intercept to zero?
I'm using bptest function of lmtest package to use Breusch-Pagan test.
I get a strange result, doing the follow:
...
- 2,697
1
vote
1
answer
42
views
Formula for comparing the youth of different groups?
For purely personal reasons, I recently tried to write a Ruby script that pulled information about various school rosters, counting the numbers of freshmen...seniors on the team and using that data to ...
- 113
3
votes
2
answers
26k
views
Given P(A) and P(B), what would be the minimum probability of the intersection?
Like if I was given a P(A) of .5 and a P(B) value of .4 how would I get the minimum of the P(A∩B)?
- 41
1
vote
1
answer
228
views
How should I characterize the "typical" variance of a large collection of variables?
For an experiment I'm analyzing, I took many measurements of many different values. (To make it concrete, let's pretend I measured the height of people from many different age groups -- I have the ...
- 113
2
votes
1
answer
695
views
Validating a predicted standard deviation
I would like to validate the standard deviation which a model reports, because I think it is underestimated, because in the procedure some model selection is involved.
After running the model on a ...
- 203
7
votes
2
answers
972
views
Model errors, residuals and heteroscedasticity
I have a quick question about the correct way to describe variance functions when seeking to cope with heteroscedasticity. As I understand it the statistical error of a model represents the departure ...
- 679
4
votes
0
answers
3k
views
4
votes
1
answer
2k
views
How can these residuals have homogeneity of variances?
I'm testing the Homogeneity of Variances with Fligner-Killeen test using the function fligner.test in stats
On the chart below I have plotted the residuals that pass this test ...
- 2,697
3
votes
1
answer
1k
views
Difference between homoscedastic and homogenic-variance data
I have a doubt regarding two tests:
Breusch–Pagan test, to detect heteroscedasticity in a series, and
Bartlett's test, to test for equal variances for samples from $k$
populations.
What are the ...
- 33
2
votes
2
answers
618
views
Predicting a maximum value with little data
My problem is i'm trying to figure out how many servers might be required to handle a theoretical maximal load of data requests. To do that I need to know what the maximum number of requests in a ...
- 123
2
votes
0
answers
574
views
How to detect changepoint with a bit of tolerance?
I'm using the changepoint package in R because I need to check if the variance is stable or if there are some breaks inside. The function cpt.var does the job well but there is not a parameter to set ...
- 2,697
3
votes
1
answer
122
views
How to assess prevalence of grossly inaccurate data in recorded body weights in medical records?
I have around 5 million observations of weights of patients over the course of a year. Some patients have one measurement during that year and others have 30-40 (or more). I've noticed a great deal ...
- 31
0
votes
1
answer
12k
views
How to interpret variance ratio test results?
I should do Variance Ratio Test on two vectors in R.
I found the a builtin function: var.test but I don't know how to interpret its results (p-value).
What result do I have to wait if these two ...
- 2,697
4
votes
1
answer
285
views
Covariance and variance relation
I collected 3D velocity data in a river. the recorded timeseries of velocity components $(u,v,w)$ contains turbulent and mean part. Reynolds Shear Stress can be estimated from
$$u=u'+U$$
$$\...
- 505
12
votes
2
answers
3k
views
Order statistics (e.g., minimum) of infinite collection of chi-square variates?
This is my first time here, so please let me know if I can clarify my question in any way (incl. formatting, tags, etc.). (And hopefully I can edit later!) I tried to find references, and tried to ...
- 696