Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

Filter by
Sorted by
Tagged with
2
votes
4answers
600 views

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 ...
44
votes
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.
2
votes
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 ...
3
votes
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 ...
1
vote
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 ...
14
votes
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 ...
2
votes
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 ...
5
votes
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 ...
7
votes
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 ...
17
votes
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 ...
4
votes
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 ...
4
votes
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 ...
49
votes
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 ...
35
votes
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?
5
votes
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 ...
188
votes
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?
8
votes
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 ...
65
votes
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?
16
votes
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 ...
24
votes
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)?
23
votes
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 ...
34
votes
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?

1
155 156 157 158
159