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Abstract In this note we reconsider the closure problem in the convolution equivalent class of distributions S ( γ ) , γ ≥ 0 . We show that, if F… Click to show full abstract
Abstract In this note we reconsider the closure problem in the convolution equivalent class of distributions S ( γ ) , γ ≥ 0 . We show that, if F , G ∈ L ( γ ) , then inclusions of F ⁎ G , FG and p F + ( 1 − p ) G for all (some) p ∈ ( 0 , 1 ) into the class S ( γ ) are equivalent. Also, we provide an example, which shows that p F + ( 1 − p ) G can be in S ( γ ) even if F and G are not in S ( γ ) .
Keywords:
class;
closure property;
class distributions;
convolution equivalent;
equivalent class
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2020
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!