# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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4answers
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### Ranking distributional data by similarity

The question in short: What methods can be used to quantify distributional relationships between data when the distribution is unknown? Now the longer story: I have a list of distributions and would ...
8answers
58k 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.
4answers
417 views

### Modeling success rate with gaussian distribution

In many papers I see data representing a rate of success (i.e a number between 0 and 1) modeled as a gaussian. This is clearly a sin (the range of variation of the gaussian is all of R), but how bad ...
2answers
984 views

### Density function for a multivariate Bernoulli-like distribution

I'm looking for a distribution to model a vector of $k$ binary random variables, $X_1, \ldots, X_k$. Suppose I have observed that $\sum_i X_i = n$. In this case I do not want to treat them as ...
1answer
443 views

### Approximating density function for a non-normal distribution

My question is actually quite short, but I'll have to start by describing the context since I am not sure how to directly ask it. Consider the following "game": We have a segment of length n ("large ...
4answers
9k views

### Questions about KL divergence?

I am comparing two distributions with KL divergence which returns me a non-standardized number that, according to what I read about this measure, is the amount of information that is required to ...
2answers
2k views

### What would the calculated value of the standard deviation of a uniform distribution be?

A colleague wants to compare models that use either a Gaussian distribution or a uniform distribution and for other reasons needs the standard devation of these two distributions to be equal. In R I ...
3answers
2k views

### Is Spearman's correlation coefficient usable to compare distributions?

I have distributions from two different data sets and I would like to measure how similar their distributions (in terms of their bin frequencies) are. In other words, I am not interested in the ...
3answers
1k views

### Nonhomogeneous Poisson and Heavy tail inter arrival time distribution

What is the relationship between a Nonhomogeneous Poisson process and a process that has heavy tail distribution for its inter arrival times? Any pointer to a resource that can shed some light on ...
5answers
5k 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 ...
2answers
5k views

### Why (or when) to use the log-mean?

I am looking at a scientific paper in which a single measurement is calculated using a logarithmic mean 'triplicate spots were combined to produce one signal by taking the logarithmic mean of ...
1answer
348 views

### To what extent can we call a Geometric Distribution a Geometric Density [duplicate]

In some papers, for example in "The Geometric Density with Unknown Location Parameter" by Klotz, a Geometric Distribution is called a Geometric Density. For me, this claim looks erroneous, however ...
6answers
13k 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 ...
2answers
118k 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?
1answer
148 views

### What approach could be used for modelling virus infections?

I'm a physics graduate who ended up doing infosec so most of the statistics I ever learned is useful for thermodynamics. I'm currently trying to think of a model for working out how many of a ...
8answers
387k 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?
4answers
783 views

### Why is the average of the highest value from 100 draws from a normal distribution different from the 98th percentile of the normal distribution?

Why is the average of the highest value from 100 draws from a normal distribution different from the 98% percentile of the normal distribution? It seems that by definition that they should be the ...
3answers
74k views

### How is the minimum of a set of IID random variables distributed?

If $X_1, ..., X_n$ are independent identically-distributed random variables, what can be said about the distribution of $\min(X_1, ..., X_n)$ in general?
2answers
5k views

### Modelling a Poisson distribution with overdispersion

I have a data set that I'd expect to follow a Poisson distribution, but it is overdispersed by about 3-fold. At the present, I'm modelling this overdispersion using something like the following code ...
3answers
86k views

### Finding the PDF given the CDF

How can I find the PDF (probability density function) of a distribution given the CDF (cumulative distribution function)?
5answers
41k 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 ...
7answers
32k 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?