Limit theorems for some classes of power series type distributions
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Aleksandr N. Timashev
Abstract
Several classes of distributions of power series type with finite and infinite radii of convergence are considered. For such distributions local limit theorems are obtained as the parameter of distribution tends to the right end of the interval of convergence. For the case when the convergence radius equals to 1, we prove an integral limit theorem on the convergence of distributions of random variables (1 − x)ξxas x → 1− to the gamma-distribution (ξx is a random variable with corresponding distribution of the power series type). The proofs are based on the steepest descent method.
Originally published in Diskretnaya Matematika (2018) 30, №4, 134–145 (in Russian).
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Articles in the same Issue
- Frontmatter
- Completeness criterion for the enumeration closure operator in three-valued logic
- Classification of distance-transitive orbital graphs of overgroups of the Jevons group
- Necessary conditions of applicability of Gaussian elimination to systems of equations over quasigroups
- The generalized complexity of linear Boolean functions
- On some implicitly precomplete classes of monotone functions in Pk
- Trees without twin-leaves with smallest number of maximal independent sets
- Limit theorems for some classes of power series type distributions
Articles in the same Issue
- Frontmatter
- Completeness criterion for the enumeration closure operator in three-valued logic
- Classification of distance-transitive orbital graphs of overgroups of the Jevons group
- Necessary conditions of applicability of Gaussian elimination to systems of equations over quasigroups
- The generalized complexity of linear Boolean functions
- On some implicitly precomplete classes of monotone functions in Pk
- Trees without twin-leaves with smallest number of maximal independent sets
- Limit theorems for some classes of power series type distributions
