A Fresh Approach to a Special Type of the Luria–Delbrück Distribution

The mutant distribution that accommodates both fitness and plating efficiency is an important class of the Luria–Delbrück distribution. Practical algorithms for computing this distribution do not coincide with the theoretically most elegant ones, as existing generic methods often either produce unre...

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Bibliographic Details
Published in:Axioms 2022-12, Vol.11 (12), p.730
Main Author: Zheng, Qi
Format: Article
Language:English
Subjects:
Algorithms
Apoptosis
Asymptotic methods
Asymptotic properties
Cell growth
Distribution (Probability theory)
Efficiency
Experiments
fitness
hypergeometric function
Hypergeometric functions
Laboratories
Mathematical research
Mutation
mutation rate
plating efficiency
Probability
Production methods
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Summary:The mutant distribution that accommodates both fitness and plating efficiency is an important class of the Luria–Delbrück distribution. Practical algorithms for computing this distribution do not coincide with the theoretically most elegant ones, as existing generic methods often either produce unreliable results or freeze the computational process altogether when employed to solve real-world research problems. Exploiting properties of the hypergeometric function, this paper offers an algorithm that considerably expands the scope of application of this important class of the Luria–Delbrück distribution. An integration method is also devised to complement the novel algorithm. Asymptotic properties of the mutant probability are derived to help gauge the new algorithm. An illustrative example and simulation results provide further guidelines on the use of the new algorithm.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms11120730