# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### Distribution of inverse Wishart to a power?

In a related question, I had asked about the norm induced by an inverse Wishart matrix. I am interested in generalizing that result somewhat. Let $A\sim\mathcal{W}_p\left(I,n\right)$, a Wishart matrix ...
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### How do I identify the “Long Tail” portion of my distribution?

I have a number of series that would typically be described as normal skewed or Gamma distributed. For example, say I have a group of customers and have calculated their spend over a fixed length of ...
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### Is there an asymptotic distribution expansion that does not go negative when truncated?

I am looking into a problem where I have a distribution that converges to the normal distribution as its parameters become large. I am looking at the rate of this convergence, and seeking to describe ...
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### Correcting Sample Selection Bias given actual Distribution

I have two datasets, both from the same population: The samples from the first survey are quite representative of the underlying truth. However, the second survey comes with a change in distribution ...
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### Exact Null Distribution with Ties

I am interested in deriving exact null distributions for small-sample test statistics with non-trivial ties. Not fundamentally continuous variables that happen to have a few repeated values, but ...
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### Probability distribution models compatible with quantile regression

I am familiarizing myself with quantile regression. I understand it is first and foremost an estimation method such as e.g. OLS. But I wonder about the probability distribution models for which ...
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### Expectation of a strictly increasing function

Assume that $X_1$ and $X_2$ are two i.i.d. random variables with pdf $f$. Also, assume that $a$ and $b$ are two fixed real numbers such that $a>b$. If $g$ is a strictly increasing function, do I ...
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### Processes behind statistical distribution laws: a compendium?

The simple processes that "explain" the binomial, Gaussian or Poisson distribution are relatively well-known. Johnson or shot noises may be known in restricted area of science. Sometimes, a ...
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### How can I calculate the probability that the product of two independent random variables does not exceed $L$?

I have one variable, $X$, which is provided hourly for a period of one month (720 total values in the series). I have another variable, $Y$, which is provided quarterly (for which I am provided the ...
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### Use Chi-Squared or Binomial Test if Distribution is not Known?

Suppose you have a set of data (eg. [a, b, a, a, b, b, etc.]), and you have the suspicion that the set of data follows the binomial distribution. Your Null Hypothesis is: The probability of success ...
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### Are there useful distributions for ternary variables (e.g. $-1,0,1$ data)?

The title says it. If one wishes to analyze ternary outcomes—that is categorical outcomes with specifically three values (-1,0,1)—are $\chi^{2}$ / contingency table tests and multinomial-logistic ...
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### Zipf's vs Self-similar: are they really the same

Recently I ran into a test using both zipf's and self-similar generated datasets. I followed the description from Jim Gray's paper on generating such datasets (Quickly Generating Billon-Record ...
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### Joint distribution of column sums when row sums are fixed

Suppose I have an $m$ by $n$ table $X_{ij} \in \{0,1\}$, where in each row, $r$ randomly chosen entries are set to 1 (the rest are 0), i.e. $\sum_j X_{ij}=r$. I know that e.g. the column sum \$\sum_i ...
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### How to define and model consumption bundles?

Imagine an a la carte buffet with n different rooms. On entering the buffet you pick a room (let's say American, Mexican or Italian food) where you stay for the duration of your visit. Once in a room,...