A distribution is a mathematical description of *probabilities* or *frequencies.*
36
votes
4answers
2k views
What is intuition behind beta distribution?
Disclaimer: I'm not statistician but rather software engineer. Most of my knowledge in statistics comes from self-education, thus I still have many gaps in understanding concepts that may seem trivial ...
33
votes
6answers
32k views
In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?
Am I looking for a better behaved distribution for the independent variable in question, or to reduce the effect of outliers, or something else?
29
votes
6answers
2k views
Motivation for Kolmogorov distance between distributions
There are many ways to measure how similar two probability distributions are. Among methods which are popular (in different circles) are:
the Kolmogorov distance: the sup-distance between the ...
25
votes
3answers
3k views
A Probability distribution value exceeding 1 is OK?
On the Wikipedia page about naive bayes classifiers here there is this line "P(height|male) = 1.5789 (A probability distribution over 1 is OK. It is the area under the bell curve that is equal to 1.)" ...
21
votes
7answers
4k views
What is normality?
In many different statistical methods there is an "assumption of normality". What is "normality" and how do I know if there is normality?
21
votes
5answers
10k views
How to identify a bimodal distribution?
I understand that once we plot the values as a chart, we can identify a bimodal distribution by observing the twin-peaks, but how does one find it programmatically? (I am looking for an algorithm.)
20
votes
5answers
3k 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 mom or child how would one go about it?
It's a concept ...
19
votes
5answers
757 views
Fake uniform random numbers: More evenly distributed than true uniform data
I'm looking for a way to generate random numbers that appear to be uniform distributed -- and every test will show them to be uniform -- except that they are more evenly distributed than true uniform ...
19
votes
2answers
794 views
What's so 'moment' about 'moments' of a probability distribution?
I KNOW what moments are and how to calculate them and how to use the moment generating function for getting higher order moments. Yes, I know the math.
Now that I need to get my statistics knowledge ...
19
votes
2answers
881 views
Does the distribution $\log(1 + x^{-2}) / 2\pi$ have a name?
I ran across this density the other day. Has someone given this a name?
$f(x) = \log(1 + x^{-2}) / 2\pi$
The density is infinite at the origin and it also has fat tails. I saw it used as a prior ...
17
votes
8answers
3k views
How can I efficiently model the sum of Bernoulli random variables?
I am modeling a random variable ($Y$) which is the sum of some ~15-40k independent Bernoulli random variables ($X_i$), each with a different success probability ($p_i$). Formally, $Y=\sum X_i$ where ...
17
votes
5answers
3k views
If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?
I'm sure I've got this completely wrapped round my head, but I just can't figure it out.
The t-test compares two normal distributions using the Z distribution. That's why there's an assumption of ...
17
votes
2answers
944 views
Distributions other than the normal where mean and variance are independent
I was wondering if there are any distributions besides the normal where the mean and variance are independent of each other (or in other words, where the variance is not a function of the mean).
17
votes
1answer
978 views
For which distributions are the parameterizations in BUGS and R different?
I have found some distributions for which BUGS and R have different parameterizations: Normal, log-Normal, and Weibull.
For each of these, I gather that the second parameter used by R needs to be ...
16
votes
9answers
1k views
How do I figure out what kind of distribution represents this data on ping response times?
i've sampled a real world process, network ping times. The "round-trip-time" is measured in milliseconds. Results are plotted in a histogram:
Ping times have a minimum value, but a long upper tail.
...
16
votes
2answers
2k views
Understanding the parameters inside the Negative Binomial Distribution
I was trying to fit my data into various models and figured out that the fitdistr function from library MASS of ...
16
votes
2answers
462 views
Can we see shape of normal curve somewhere in nature?
I do not want to know if some phenomena in nature have normal distribution, but whether we can somewhere see shape of normal curve as we can see it for example in Galton box. See this figure from ...
15
votes
3answers
361 views
How to sample from $c^a d^{a-1} / \Gamma(a)$?
I want to sample according to a density
$$
f(a) \propto \frac{c^a d^{a-1}}{\Gamma(a)} 1_{(1,\infty)}(a)
$$
where $c$ and $d$ are strictly positive.
(Motivation: This could be useful for Gibbs ...
15
votes
1answer
2k views
Empirical Relationship Between Mean, Median and Mode
For a unimodal distribution which is moderately skewed, we have the following empirical relationship between mean, mode and median:
(Mean-Mode) ~ 3(Mean-Median)
Could someone please explain how the ...
14
votes
4answers
903 views
What are good data visualization techniques to compare distributions?
I am writing my PhD thesis and I've realized that I rely excessively in box plots in order to compare distributions. Which other alternatives do you like for achieving this task?
I'd also like to ask ...
14
votes
3answers
716 views
Weakly informative prior distributions for scale parameters
I have been using log normal distributions as prior distributions for scale parameters (for normal distributions, t distributions etc.) when I have a rough idea about what the scale should be, but ...
13
votes
2answers
620 views
Can two random variables have the same distribution, yet be almost surely different?
Is it possible that two random variables have the same distribution and yet they are almost surely different?
13
votes
8answers
9k views
How can I test if given samples are taken from a Poisson distribution?
I know of normality tests, but how do I test for "Poisson-ness"?
I have sample of ~1000 non-negative integers, which I suspect are taken from a Poisson distribution, and I would like to test that.
13
votes
2answers
382 views
How to know which probability distribution to expect?
Currently I am analyzing social networks (not virtual) and I am observing the connections between people. If a person would choose another person to connect with randomly, the number of connections ...
12
votes
2answers
296 views
Which distributions have closed-form solutions for maximum likelihood estimation?
Which distributions have closed-form solutions for the maximum likelihood estimates of the parameters from a sample of independent observations?
12
votes
3answers
527 views
Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical?
In May 2010 Wikipedia user Mcorazao added a sentence to the skewness article that "A zero value indicates that the values are relatively evenly distributed on both sides of the mean, typically but not ...
12
votes
5answers
569 views
Comparing the variance of paired observations
I have $N$ paired observations ($X_i$, $Y_i$) drawn from a common unknown distribution, which has finite first and second moments, and is symmetric around the mean.
Let $\sigma_X$ the standard ...
11
votes
3answers
2k views
Are there default functions for discrete uniform distributions in R?
Most standard distributions in R have a family of commands - pdf/pmf, cdf/cmf, quantile, random deviates (for example- dnorm, pnorm, qnorm, rnorm).
I know it's easy enough to make use of some ...
11
votes
8answers
5k views
Can the standard deviation of non-negative data exceed the mean?
I have some triangulated 3D meshes. The statistics for the triangle areas are:
Min 0.000
Max 2341.141
Mean 56.317
Std dev 98.720
So, does it mean anything particularly useful about the standard ...
11
votes
4answers
676 views
Analysing wind data with R
Hi i am analaysing wind data for estimating energy from a wind turbine.
I have taken 10 years of wind data and graphed a histogram;
my second stage was to fit a Weibull distribution to the data.
I ...
11
votes
2answers
723 views
Why does the supremum of the Brownian bridge have the Kolmogorov–Smirnov distribution?
The Kolmogorov–Smirnov distribution is known from the Kolmogorov–Smirnov test. However, it is also the distribution of the supremum of the Brownian bridge.
Since this is far from obvious (to me), I ...
11
votes
3answers
963 views
Moments of a distribution - any use for partial or higher moments?
It is usual to use second, third and fourth moments of a distribution to describe certain properties. Do partial moments or moments higher than the fourth describe any useful properties of a ...
11
votes
1answer
12k views
What is the difference between the Shapiro-Wilk test of normality and the Kolmogorov-Smirnov test of normality?
What is the difference between the Shapiro-Wilk test of normality and the Kolmogorov-Smirnov test of normality? When will results from these two methods differ?
11
votes
1answer
168 views
Deriving Negentropy. Getting stuck
So, this question is somewhat involved but I have painstakingly tried to make it as straight-forward as possible.
Goal: Long story short, there is a derivation of negentropy that does not involve ...
11
votes
1answer
1k views
Kullback–Leibler vs Kolmogorov-Smirnov distance
I can see that there are a lot of formal differences between Kullback–Leibler vs Kolmogorov-Smirnov distance measures.
However, both are used to measure the distance between distributions.
Is there ...
11
votes
1answer
259 views
Is centering needed when bootstrapping the sample mean?
When reading about how to approximate the distribution of the sample mean I came across the nonparametric bootstrap method. Apparently one can approximate the distribution of $\bar{X}_n-\mu$ by the ...
10
votes
3answers
374 views
Testing data against a known distribution
I asked a question similar to this a while ago, and the general answer was "your question is too vague". So let me try again with a little more detail...
I have written a program which generates ...
10
votes
2answers
3k views
How to calculate Zipf's law coefficient from a set of top frequencies?
I have several query frequencies, and I need to estimate the coefficient of Zipf's law. These are the top frequencies:
...
10
votes
1answer
324 views
What is the community's take on the Fourth Quadrant?
Nassim Taleb, of Black Swan fame (or infamy), has elaborated on the concept and developed what he calls "a map of the limits of Statistics". His basic argument is that there is one kind of decision ...
10
votes
1answer
779 views
What is the real answer to the Birthday question?
"How large must a class be to make the probability of finding two people with the same birthday at least 50%?"
I have 360 friends on facebook, and, as expected, the distribution of their birthdays is ...
10
votes
5answers
2k views
Assessing the significance of differences in distributions
I have two groups of data. Each with a different distribution of multiple variables. I'm trying to determine if these two groups' distributions are different in a statistically significant way. I ...
10
votes
2answers
241 views
What's the name of this discrete distribution (recursive difference equation) I derived?
I came across this distribution in a computer game and wanted to learn more about its behaviour. It comes from the decision as to whether a certain event should occur after a given number of player ...
10
votes
3answers
227 views
Dealing with 0,1 values in a beta regression
I have some data in [0,1] which I would like to analyze with a beta regression.
Of course something needs to be done to accommodate the 0,1 values. I dislike
modifying data to fit a model. also I ...
10
votes
1answer
387 views
What are the pros and cons of learning about a distribution algorithmically (simulations) versus mathematically?
What are the pros and cons of learning about a distribution's properties algorithmically (via computer simulations) versus mathematically?
It seems like computer simulations can be an alternative ...
10
votes
3answers
414 views
What are the distributions on the positive k-dimensional quadrant with parametrizable covariance matrix?
Following zzk's question on his problem with negative simulations, I am wondering what are the parametrized families of distributions on the positive k-dimensional quadrant, $\mathbb{R}_+^k$ for which ...
10
votes
1answer
476 views
Maximum likelihood estimators for a truncated distribution
Consider $N$ independent samples $S$ obtained from a random variable $X$ that is assumed to follow a truncated distribution (e.g. a truncated normal distribution) of known (finite) minimum and maximum ...
10
votes
2answers
389 views
How to scale violin plots for comparisons?
I'm trying to draw violin plots and wondering if there is an accepted best practice for scaling them across groups. Here are three options I've tried using the R ...
10
votes
1answer
90 views
Long-tailed distribution of time events
Suppose you have the logs of a web server. In these logs you have tuples of this kind:
...
9
votes
5answers
15k views
How to perform a test using R to see if data follows normal distribution
I have a data set with following structure:
a word | number of occurrence of a word in a document | a document id
How can I perform a test for normal ...
9
votes
7answers
2k views
What are some alternatives to a boxplot?
I am working on creating a website, which displays the census data for a user selected Polygons & would like to graphically show the distribution of various parameters (one graph per parameter).
...
