# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

8,413 questions
Filter by
Sorted by
Tagged with
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 ...
6k 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 ...
361 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 ...
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 ...
127k 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?
150 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 ...
425k 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?
791 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 ...
80k 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?
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 ...
93k 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)?