# Tagged Questions

A distribution is a mathematical description of *probabilities* or *frequencies.*

8k views

### What is the intuition behind beta distribution?

Disclaimer: I'm not a statistician but a 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 ...
45k 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?
4k views

### A Probability distribution value exceeding 1 is OK?

On the Wikipedia page about naive Bayes classifiers, there is this line: $p(\mathrm{height}|\mathrm{male}) = 1.5789$ (A probability distribution over 1 is OK. It is the area under the bell curve ...
3k 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 ...
6k 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?
5k 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 ...
12k 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.)
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### 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 ...
1k 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 ...
924 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 ...
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 ...
14k 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.
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### 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 ...
1k 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 ...
3k 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 ...
308 views

### Why not report the mean of a bootstrap distribution?

When one bootstraps a parameter to get the standard error we get a distribution of the parameter. Why don't we use the mean of that distribution as a result or estimate for the parameter we are trying ...
1k 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).
2k 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. ...
425 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 ...
677 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 ...
1k 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 ...
912 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 ...
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 ...
858 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?
3k 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 ...
433 views

### How can the number of connections be Gaussian if it cannot be negative?

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 within a ...
7k 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 ...
378 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 ...
2k views

### Confidence interval for Bernoulli sampling

I have a random sample of Bernoulli random variables $X_1 ... X_N$, where $X_i$ are i.i.d. r.v. and $P(X_i = 1) = p$, and $p$ is an unknown parameter. Obviously, one can find an estimate for $p$: ...
17k 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?
736 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 ...
2k views

### Bootstrap vs. Jackknife

Both bootstrap and jackknife methods can be used to estimate bias and standard error of an estimate and mechanisms of both resampling methods are not huge different: sampling with replacement vs. ...
1k 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 ...
666 views

### How do Bayesians compare distributions?

So, I think that I have a decent grasp of the basics of frequentist probability and statistical analysis (and how badly it can be used). In a frequentist world, it makes sense to ask such a question ...
515 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 ...
405 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?
737 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 ...
849 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 ...
855 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 ...
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 ...