Generation of cubic power-law for high frequency intra-day returns: Maximum Tsallis entropy framework

Senapati, Dilip; Karmeshu,

doi:10.1016/j.dsp.2015.09.018

Cited by 30 publications

(9 citation statements)

References 26 publications

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“…This section provides the formulation procedure of non-extensive q-Lognormal PDF. The desired PDF undergoes the difference of integral sign of the corresponding Lagrangian function, which is constructed following maximum entropy principle i.e., non-extensive q-Lognormal PDF is maximized Tsallis' entropy with normalized, first, and second moment constrains [10,9].…”

Section: Q-lognormal Probability Density Function (Pdf)mentioning

confidence: 99%

“…In this context, a framework incorporating maximum entropy principle based on non-extensive parameter 'q' defined by Tsallis' is portrayed to explain the extreme tail fluctuations of the fading signals [10,9,14,28,7]. The specification of the normalization constraint along with first and second moment constraints results in the q-Lognormal model [23] for the continuous range of parameter 'q', 1 < q < 3.…”

Section: Introductionmentioning

confidence: 99%

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An adaptive q-Lognormal model towards the computation of average channel capacity in slow fading channels

Mukherjee

Senapati

2022

Telecommun Syst

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Section: Q-lognormal Probability Density Function (Pdf)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An adaptive q-Lognormal model towards the computation of average channel capacity in slow fading channels

Mukherjee

Senapati

2022

Telecommun Syst

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Section: Q-lognormal Probability Density Function (Pdf)mentioning

confidence: 99%

“…The null hypothesis H 0 : the generated fading data is in agreement with the theoretical q-Lognormal distribution is validated by employing χ 2 -test. The value of degrees of freedom (d.f)= n -1 -1, where n=19 is the number of bins in the histogram [9] of the synthetic signal. Since, JS measure is used to estimate the parameter q, there is an unit decrement in the d.f.…”

Section: Goodness Of Fitmentioning

confidence: 99%

An adaptive q-Lognormal model towards the computation of Average Channel Capacity in slow fading channels

Mukherjee¹,

Senapati²

2021

Preprint

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The characterization of multipath fading and shadowing in wireless communication systems is essential towards the evaluation of various performance measures. It is well known that the statistical characterization of shadowing phenomena is captured by distributions viz., log-normal distribution, gamma distribution and other mixture distributions. However, it is observed that the log-normal distribution fails to characterize the outliers in the fading signal. The extreme fluctuations in the fading signal needs to be characterized efficiently for error free computation of the various performance metrics. In this context, this paper portrays an adaptive generalized Tsallis’ non-extensive q-Lognormal model towards the characterization of various fading channels. This model operates well with the synthesized fading signals and captures the wide range of tail fluctuations to adapt different fading scenarios. The significance and applicability of the proposed novel q- Lognormal model in capturing the slow fading channels is validated using different statistical tests viz., chi-square test and symmetric JS measure. Furthermore, essential performance measures viz., the average channel capacity, closed form expression of cumulative distribution function (CDF) in terms of Gauss-Hypergeometric function 2 F 1 [a ; b ; c; z], higher order moments corresponding to q-Lognormal channel capacity and coefficient of variation is evaluated corresponding to the proposed q-Lognormal model performing extensive Monte-Carlo simulation techniques up to O (10^7).

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“…The limiting value of H α as α → 1 is the Shannon entropy. Tsallis entropy is more suitable than Shannon entropy in non-extensive system and long-range interactions [173]. Tsallis entropy is defined as…”

Section: Shapementioning

confidence: 99%

Pathological Brain Detection by Artificial Intelligence in Magnetic Resonance Imaging Scanning (Invited Review)

Wang¹,

Zhang²,

Zhan³

et al. 2016

PIER

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Abstract-(Aim) Pathological brain detection (PBD) systems aim to assist and even replace neuroradiologists to make decisions for patients. This review offers a comprehensive and quantitative comparison for PBD systems by artificial intelligence in magnetic resonance imaging (MRI) scanning. (Method) We first investigated four categories of brain diseases, including neoplastic disease, neurodegenerative disease, cerebrovascular disease, and inflammation. Next, we introduced important MRI techniques, such as the shimming, water and fat suppression, and three advanced imaging modalities (functional MRI, diffusion tensor imaging, and magnetic resonance spectroscopic imaging). Then, we discussed four image preprocessing techniques (image denoising, slice selection, brain extraction, spatial normalization, and intensity normalization), seven feature representation techniques (shape, moment, wavelet, statistics, entropy, gray level co-occurrence matrix, and Fourier transform), and two dimension reduction techniques (feature selection and feature extraction). Afterwards, we studied classification related methods: six learning models (decision tree, extreme learning machine, k-nearest neighbors, naive Bayes classifier, support vector machine, feed-forward neural network), five kernel functions (linear, homogeneous and inhomogeneous polynomial, radial basis function, and sigmoid), and three types of optimization methods (evolutionary algorithm, stochastic optimization, and swarm intelligence). (Results) We introduced three benchmark datasets and used K-fold stratified cross validation to avoid overfitting. We presented a detailed quantitative comparison among 44 state-of-theart PBD algorithms and discussed their advantages and limitations. (Discussions) Artificial intelligence is now making stride in the PBD field and enjoys a fair amount of success. In the future, semi-supervised learning and transfer learning techniques may be potential breakthroughs to develop PBD systems.

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Generation of cubic power-law for high frequency intra-day returns: Maximum Tsallis entropy framework

Cited by 30 publications

References 26 publications

An adaptive q-Lognormal model towards the computation of average channel capacity in slow fading channels

An adaptive q-Lognormal model towards the computation of average channel capacity in slow fading channels

An adaptive q-Lognormal model towards the computation of Average Channel Capacity in slow fading channels

Pathological Brain Detection by Artificial Intelligence in Magnetic Resonance Imaging Scanning (Invited Review)

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