Estimation of Parameters of Fractional Stable Distributions

Bening, V. E.; Korolev, V. Yu.; Kolokoltsov, Vassili N.; Saenko, V. V.; Учайкин, В. В.; Золотарев, В. М.

doi:10.1023/b:joth.0000036313.13319.cf

Cited by 14 publications

(12 citation statements)

References 7 publications

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“…By (4) with a constant C uniformly for all x and n > 0 (in fact it holds for large enough n by (4) and is extended to all n, because all p(x, dy) are probability measures). Hence for an arbitrary ε < 1 one has…”

Section: Limit Theorems For Position-dependent Random Walks For a Vementioning

confidence: 99%

Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics

Kolokoltsov¹

2009

Theory Probab. Appl.

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Abstract. Functional limit theorems for continuous-time random walks (CTRW) are found in the general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional dynamics. Probabilistic interpretation of generalized fractional evolution is given in terms of the random time change (subordination) by means of hitting times processes.

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Section: Limit Theorems For Position-dependent Random Walks For a Vementioning

confidence: 99%

Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics

Kolokoltsov¹

2009

Theory Probab. Appl.

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“…The first method has been described in the work [19] and the estimators were obtained on basis of the method of moments. However, it has been established that usage of these estimators lead to wrong parameters values.…”

Section: Fractional-stable Laws and Estimators Of Their Parametersmentioning

confidence: 99%

Дробно-Устойчивая Статистика Экспрессии Генов В Экспериментальных Данных Секвенирования Нового Поколения

Saenko¹

2016

Math.Biol.Bioinf.

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Abstract.As has been shown in the previous article [1] an application of class of the fractional-stable laws to the genes expression results obtained by DNA-microarrays leads to poor agreement between experimental and theoretical distributions. This difference can be explained by the imperfection of the technology of the gene expression determination. In this article the distributions of the gene expression obtained by Next Generation Sequence technology are investigated. In this technology the determination technique of the gene expression differs from the DNA-microarrays technology. This results to more qualitative results of an approximation. In particular, it is established that the probability density function of the gene expression has a form of shift-scale mixture of probability laws, where one of the components of the mixture is the fractional-stable distribution.

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“…where C ≃ 0.5772156649015328606065 is the Euler's constant. Recall the following formula from [4] and [22] for the higher log-moments of |S|:…”

Section: Stable Representation Of the Random Variable Lmentioning

confidence: 99%

An estimation procedure for the Linnik distribution

Cahoy

2011

Stat Papers

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Estimation of Parameters of Fractional Stable Distributions

Cited by 14 publications

References 7 publications

Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics

Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics

Дробно-Устойчивая Статистика Экспрессии Генов В Экспериментальных Данных Секвенирования Нового Поколения

An estimation procedure for the Linnik distribution

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