Statistical Analysis of Hairpins and BasePairs in RNA Secondary Structures
AJ Bu, Manuel Kauers, Doron Zeilberger
TL;DR
This paper provides detailed asymptotic statistical properties of hairpins and basepairs in RNA secondary structures, demonstrating their joint distribution approaches a bi-variate normal distribution with a specific correlation.
Contribution
It derives precise asymptotic formulas for moments and establishes the joint distribution of hairpins and basepairs in RNA structures.
Findings
Expectations, variances, and covariance are explicitly calculated.
The joint distribution converges to a bi-variate normal distribution.
Correlation between hairpins and basepairs is approximately 0.2123.
Abstract
We derive precise asymptotic expressions for the expectations, variances, covariance, and quite a few further mixed moments for the number of hairpins and the number of basepairs in RNA secondary structures, and give convincing evidence that the central-scaled distribution of the pair of random variables (hairpins, basepairs) tends in distribution to the bi-variate normal distribution with correlation
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Taxonomy
TopicsBayesian Methods and Mixture Models · RNA and protein synthesis mechanisms · Stochastic processes and statistical mechanics