Gamma, Gaussian and Poisson approximations for random sums using size-biased and generalized zero-biased couplings

We derive upper bounds for the total variation distance, d, between the distributions of two random sums of non-negative integer-valued random variables. The main results are then applied to some important random sums, including cluster binomial and cluster multinomial distributions, to obtain bounds on approximating them to suitable Poisson or compound Poisson distributions. These bounds are generally better than the known results on Poisson and compound Poisson approximations. We also obtain a lower bound for d and illustrate it with an example.

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Poisson and compound Poisson approximations for random sums of random variables

Journal of Applied Probability ◽

10.2307/3215270 ◽

1996 ◽

Vol 33 (1) ◽

pp. 127-137 ◽

Cited By ~ 10

Author(s):

P. Vellaisamy ◽

B. Chaudhuri

Keyword(s):

Lower Bound ◽

Total Variation ◽

Random Variables ◽

Upper Bounds ◽

Random Sums ◽

Compound Poisson ◽

Sums Of Random Variables ◽

Variation Distance ◽

Poisson Approximations ◽

Better Than

We derive upper bounds for the total variation distance, d, between the distributions of two random sums of non-negative integer-valued random variables. The main results are then applied to some important random sums, including cluster binomial and cluster multinomial distributions, to obtain bounds on approximating them to suitable Poisson or compound Poisson distributions. These bounds are generally better than the known results on Poisson and compound Poisson approximations. We also obtain a lower bound for d and illustrate it with an example.

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Graph-based variational auto-encoder for generalized zero-shot learning

Proceedings of the 2nd ACM International Conference on Multimedia in Asia ◽

10.1145/3444685.3446283 ◽

2021 ◽

Author(s):

Jiwei Wei ◽

Yang Yang ◽

Xing Xu ◽

Yanli Ji ◽

Xiaofeng Zhu ◽

...

Keyword(s):

Generalized Zero

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Two-Level Adversarial Visual-Semantic Coupling for Generalized Zero-shot Learning

2021 IEEE Winter Conference on Applications of Computer Vision (WACV) ◽

10.1109/wacv48630.2021.00314 ◽

2021 ◽

Author(s):

Shivam Chandhok ◽

Vineeth N Balasubramanian

Keyword(s):

Generalized Zero

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Generalized Zero-shot Learning with Multi-source Semantic Embeddings for Scene Recognition

Proceedings of the 28th ACM International Conference on Multimedia ◽

10.1145/3394171.3413568 ◽

2020 ◽

Author(s):

Xinhang Song ◽

Haitao Zeng ◽

Sixian Zhang ◽

Luis Herranz ◽

Shuqiang Jiang

Keyword(s):

Scene Recognition ◽

Generalized Zero

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Generalized Zero-shot Learning via Multi-modal Aggregated Posterior Aligning Neural Network

IEEE Transactions on Multimedia ◽

10.1109/tmm.2020.3047546 ◽

2020 ◽

pp. 1-1

Author(s):

Xingyu Chen ◽

Jin Li ◽

Xuguang Lan ◽

Nanning Zheng

Keyword(s):

Neural Network ◽

Generalized Zero

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On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

Mathematics ◽

10.3390/math9131571 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1571

Author(s):

Irina Shevtsova ◽

Mikhail Tselishchev

Keyword(s):

Negative Binomial Distribution ◽

Binomial Distribution ◽

Law Of Large Numbers ◽

Negative Binomial ◽

Infinite Divisibility ◽

Random Sums ◽

Generalized Gamma ◽

Second Moments ◽

Large Numbers ◽

Generalized Negative Binomial Distribution

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 Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.

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Modality independent adversarial network for generalized zero shot image classification

Neural Networks ◽

10.1016/j.neunet.2020.11.007 ◽

2021 ◽

Vol 134 ◽

pp. 11-22

Author(s):

Haofeng Zhang ◽

Yinduo Wang ◽

Yang Long ◽

Longzhi Yang ◽

Ling Shao

Keyword(s):

Image Classification ◽

Adversarial Network ◽

Generalized Zero

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Asymptotic Expansions in the Exponent: a Compound Poisson Approach

Advances in Applied Probability ◽

10.1017/s0001867800028044 ◽

1997 ◽

Vol 29 (02) ◽

pp. 374-387 ◽

Cited By ~ 1

Author(s):

V. Čekanavičius

Keyword(s):

Asymptotic Expansion ◽

Large Deviations ◽

Poisson Distribution ◽

Asymptotic Expansions ◽

Compound Poisson ◽

Poisson Measures ◽

Poisson Approximations

The accuracy of the Normal or Poisson approximations can be significantly improved by adding part of an asymptotic expansion in the exponent. The signed-compound-Poisson measures obtained in this manner can be of the same structure as the Poisson distribution. For large deviations we prove that signed-compound-Poisson measures enlarge the zone of equivalence for tails.

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