# Cantor-solus and Cantor-multus Distributions

@article{Finch2020CantorsolusAC, title={Cantor-solus and Cantor-multus Distributions}, author={Steven R. Finch}, journal={ArXiv}, year={2020}, volume={abs/2003.09458} }

The Cantor distribution is obtained from bitstrings; the Cantor-solus distribution (a new name) admits only strings without adjacent 1 bits. We review moments and order statistics associated with these. The Cantor-multus distribution is introduced -- which instead admits only strings without isolated 1 bits -- and more complicated formulas emerge.

## 3 Citations

### Variance of Longest Run Duration in a Random Bitstring

- PhysicsArXiv
- 2020

While negative correlations approach zero as n approaches zero as $n \rightarrow \infty$ in the former (for clumped 1s), the limit is evidently nonzero in the latter (for separated 1s).

### C O ] 1 3 O ct 2 02 0 Covariance within Random Integer Compositions

- Mathematics
- 2020

Fix a positive integer N . Select an additive composition ξ of N uniformly out of 2N−1 possibilities. The interplay between the number of parts in ξ and the maximum part in ξ is our focus. It is not…

### Covariance within Random Integer Compositions

- MathematicsArXiv
- 2020

It is given inconclusive evidence that $\lim_{N \to \infty} \rho(N)$ is strictly less than zero; a proof of this result would imply asymptotic dependence, and the presumption in such an unforeseen outcome is retracted.

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