Sum of arbitrarily correlated Gamma random variables with unequal parameters and its application in wireless communications

Feng, Yuanhua; Wen, Miaowen; Zhang, Jun; Ji, Fei; Ning, Gengxin

doi:10.1109/iccnc.2016.7440693

Cited by 19 publications

(12 citation statements)

References 17 publications

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“…

normalΓ false(1 / 2, 2 σ_{X}^{2} false)

, and is compared with the pdf obtained through Monte Carlo simulations. Approximation 1 Let

X_{n}

, for

n = 1, 2, \dots, N

, be correlated Gamma distributed random variables with shape and scale parameters

α_{n}

and

β_{n}

, respectively [30]. Let R be the covariance matrix.…”

Section: Basic Results From Probability Theorymentioning

confidence: 99%

See 1 more Smart Citation

Statistical characterisation and analysis of differential correlation‐based frame detector

Akhlaq

Ansari²,

Lechner

et al. 2019

IET Communications

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“…

normalΓ false(1 / 2, 2 σ_{X}^{2} false)

, and is compared with the pdf obtained through Monte Carlo simulations. Approximation 1 Let

X_{n}

, for

n = 1, 2, \dots, N

, be correlated Gamma distributed random variables with shape and scale parameters

α_{n}

and

β_{n}

, respectively [30]. Let R be the covariance matrix.…”

Section: Basic Results From Probability Theorymentioning

confidence: 99%

“…It is well known that the solution to the sum of correlated Gamma random variables with different shape and scale parameters is still an open problem [30]. Therefore, to solve this problem we use an approximate solution for the sum of correlated Gamma random variables as presented in Approximation 1.…”

Section: Multi‐span Differential Correlation Statisticsmentioning

confidence: 99%

Statistical characterisation and analysis of differential correlation‐based frame detector

Akhlaq

Ansari²,

Lechner

et al. 2019

IET Communications

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“…The trivial case xk = 0 for each x ∈ Z copes with Assumption 5. Correlated Gamma variables, as well as the distributional properties of the sum of Gamma variables, have been intensively studied in the literature, and this is still an active research field [20][21][22][23], due to its relevance for information technology. At least in case of identically distributed Gamma variables-such as Γ (j) k in our framework-with ACF obeying to a power-law…”

Section: Internal Consistency and Autocorrelation In Time Seriesmentioning

confidence: 99%

Calibrating the CreditRisk+ Model at Different Time Scales and in Presence of Temporal Autocorrelation †

Giacomelli

Passalacqua

2021

Mathematics

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The CreditRisk+ model is one of the industry standards for the valuation of default risk in credit loans portfolios. The calibration of CreditRisk+ requires, inter alia, the specification of the parameters describing the structure of dependence among default events. This work addresses the calibration of these parameters. In particular, we study the dependence of the calibration procedure on the sampling period of the default rate time series, that might be different from the time horizon onto which the model is used for forecasting, as it is often the case in real life applications. The case of autocorrelated time series and the role of the statistical error as a function of the time series period are also discussed. The findings of the proposed calibration technique are illustrated with the support of an application to real data.

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“…For L > 2, the general expression ∑ l ξ l,nr is the sum of correlated gamma random variables and is distributed according to a complex infinite power series [40]. As a computationally cheap yet accurate approximation, the sum of correlated gamma random variables can be accurately approximated as a gamma random variable by matching the first two moments [41]. In a few straightforward steps, these moments can be derived as (21) and the CDF is expressed in (20).…”

Section: Appendix a The Proof Of The Bound (19)mentioning

confidence: 99%

Space–Time Signal Design for Multilevel Polar Coding in Slow Fading Broadcast Channels

Khoshnevis

Marsland

Jafarkhani

et al. 2019

IEEE Trans. Commun.

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Slow fading broadcast channels can model a wide range of applications in wireless networks. Due to delay requirements and the unavailability of the channel state information at the transmitter (CSIT), these channels for many applications are non-ergodic. The appropriate measure for designing signals in non-ergodic channels is the outage probability. In this paper, we provide a method to optimize STBCs based on the outage probability at moderate SNRs.Multilevel polar coded-modulation is a new class of coded-modulation techniques that benefits from low complexity decoders and simple rate matching. In this paper, we derive the outage optimality condition for multistage decoding and propose a rule for determining component code rates. We also derive an upper bound on the outage probability of STBCs for designing the set-partitioning-based labelling. Finally, due to the optimality of the outage-minimized STBCs for long codes, we introduce a novel method for the joint optimization of short-to-moderate length polar codes and STBCs.

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Sum of arbitrarily correlated Gamma random variables with unequal parameters and its application in wireless communications

Cited by 19 publications

References 17 publications

Statistical characterisation and analysis of differential correlation‐based frame detector

Statistical characterisation and analysis of differential correlation‐based frame detector

Calibrating the CreditRisk+ Model at Different Time Scales and in Presence of Temporal Autocorrelation †

Space–Time Signal Design for Multilevel Polar Coding in Slow Fading Broadcast Channels

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