On the rate of convergence in the central limit theorem for random sums of strongly mixing random variables
Sign Up to like & getrecommendations! Published in 2018 at "Lithuanian Mathematical Journal"
DOI: 10.1007/s10986-018-9391-6
Abstract: We present upper bounds for supx ∈ ℝ|P{ZN 0 (SN = X1 + ⋯ + XN) of centered strongly mixing or uniformly strongly mixing random variables X1, X2, . . . . Here the number of summands N is a nonnegative integer-valued random variable independent… read more here.
Keywords: random variables; random sums; rate convergence; random ... See more keywords
On the Weak Laws of Large Numbers for Compound Random Sums of Independent Random Variables with Convergence Rates
Sign Up to like & getrecommendations! Published in 2021 at "Bulletin of the Iranian Mathematical Society"
DOI: 10.1007/s41980-021-00632-5
Abstract: The weak laws of large numbers are extremely intuitive and applicable results in various fields of probability theory and mathematical statistics. Compound random sums are extensions of classical random sums where the random number of… read more here.
Keywords: weak laws; random variables; random sums; laws large ... See more keywords
Precise local large deviations for heavy-tailed random sums with applications to risk models
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DOI: 10.1080/03461238.2017.1377106
Abstract: Abstract In this paper, we investigate the precise local large deviation probabilities for random sums of independent real-valued random variables with a common heavy-tailed distribution F, where is an -regularly varying function for some fixed… read more here.
Keywords: random sums; heavy tailed; precise local; local large ... See more keywords
Markov dependence in renewal equations and random sums with heavy tails
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DOI: 10.1080/15326349.2017.1375860
Abstract: ABSTRACT The Markov renewal equation is considered in the subcritical case where the matrix of total masses of the Fij has spectral radius strictly less than one, and the asymptotics of the Zi(x) is found… read more here.
Keywords: random sums; equations random; dependence renewal; renewal ... See more keywords
On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums
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DOI: 10.3390/math9131571
Abstract: We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the… read more here.
Keywords: random sums; negative binomial; binomial random; generalized gamma ... See more keywords