Closed form expression for the inverse cumulative distribution function of Nakagami distribution

Okagbue, Hilary I.; Adamu, Muminu O.; Anake, T. A.

doi:10.1007/s11276-020-02384-2

Cited by 5 publications

(4 citation statements)

References 37 publications

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“…Because this paper focuses on the concurrent execution of SCs, it simplifies the POW and other related factors in the process. e experiment mainly focuses on the following aspects of performance: (1) when the SCTs increases, the comparison of acceleration changes in each method; (2) when the conflict rate increases, the comparison of acceleration changes in each method; (3) when the number of nodes increases, the comparison of throughput changes in each method; (4) as the number of shards increases, the throughput of individual shard and the whole system changes; (5) as the number of shards increases, the storage overhead of the nodes changes; (6) the conflict records in FIS-Table change as the number of SCTs increases; (7) the Cumulative Distribution Function (CDF) [30] of the estimated execution time and actual execution time of SC is achieved; and (8) the throughput result of the security experiment. All experimental results are the average values taken after multiple executions to reduce errors.…”

Section: Methodsmentioning

confidence: 99%

Efficient Concurrent Execution of Smart Contracts in Blockchain Sharding

Wang

Liu

et al. 2021

Security and Communication Networks

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Throughput performance is a critical issue in blockchain technology, especially in blockchain sharding systems. Although sharding proposals can improve transaction throughput by parallel processing, the essence of each shard is still a small blockchain. Using serial execution of smart contract transactions, performance has not significantly improved, and there is still room for improvement. A smart contract concurrent execution strategy based on concurrency degree optimization is proposed for performance optimization within a single shard. This strategy is applied to each shard. First, it characterizes the conflicting contract feature information by executing a smart contract, analyzing the factors that affect the concurrent execution of the smart contracts, and clustering the contract transaction. Second, in shards with high transaction frequency, considering the execution time, conflict rate, and available resources of contract transactions, finding a serializable schedule of contract transactions by redundant computation and a Variable Shadow Speculative Concurrency Control (SCC-VS) algorithm for smart contract scheduling is proposed. Finally, experimental results show that the strategy increases the concurrency of smart contract execution by 39% on average and the transaction throughput of the whole system by 21% on average.

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Section: Methodsmentioning

confidence: 99%

Efficient Concurrent Execution of Smart Contracts in Blockchain Sharding

Wang

Liu

et al. 2021

Security and Communication Networks

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“…(7) can be referred to the gamma distribution differential equation (GDDE) and the solution gives the required quantile function and can be solved using the assumed initial value conditions

. Details on the review of the method and similar methodologies can be found in [ 55 , 56 , 57 , 58 , 59 ].…”

Section: Model Formulationmentioning

confidence: 99%

Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication

Okagbue

Adamu

Anake

2020

Heliyon

Self Cite

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The use of quantile functions of probability distributions whose cumulative distribution is intractable is often limited in Monte Carlo simulation, modeling, and random number generation. Gamma distribution is one of such distributions, and that has placed limitations on the use of gamma distribution in modeling fading channels and systems described by the gamma distribution. This is due to the inability to find a suitable closed-form expression for the inverse cumulative distribution function, commonly known as the quantile function (QF). This paper adopted the Quantile mechanics approach to transform the probability density function of the gamma distribution to second-order nonlinear ordinary differential equations (ODEs) whose solution leads to quantile approximation. Closed-form expressions, although complex of the QF, were obtained from the solution of the ODEs for degrees of freedom from one to five. The cases where the degree of freedom is not an integer were obtained, which yielded values closed to the R software values via Monte Carlo simulation. This paper provides an alternative for simulating gamma random variables when the degree of freedom is not an integer. The results obtained are fast, computationally efficient and compare favorably with the machine (R software) values using absolute error and Kullback-Leibler divergence as performance metrics.

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“…The design of a function to approximate these functions typically involves a trade-off between accuracy and complexity. Achieving high accuracy often necessitates complex expressions or multi-term polynomials, as evidenced in prior studies [11,12,16,22,23,31,32,33]. Furthermore, today meta-heuristic algorithms are widely used in solving optimization problems with high complexity, if the problem can be implemented as an optimization problem, these algorithms can provide high quality solutions.…”

Section: Introductionmentioning

confidence: 99%

New Mathematical Approximations for the Cumulative Normal Distribution Function

Etesami,

Madadi,

Keynia

et al. 2024

Preprint

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The normal cumulative distribution function and its derivatives, such as the error function, the Q-function, and the Mills ratio, are widely used in engineering, mathematics, statistics, computer science, diffusion theory, communication theory, physics, and chemistry. However, their non-closed form nature has led to the development of new approximations with varying levels of accuracy and complexity. These new approximations are often more accurate; nevertheless, they can also be more complex, which may limit their practical utility. In this article, a new approach for approximating is proposed. which combines Taylor series expansion and logistic function to create an initial approximation, to enhance the accuracy of the initial approximation, the Hunter-Prey Optimization algorithm is utilized to minimize both the maximum absolute error and the mean absolute error, leading to a significantly more precise approximation. Furthermore, this algorithm is employed to enhance the accuracy of other existing approximations introduced by researchers. The results showed that the improved approximations have much higher accuracy. To show the effectiveness of the new findings of this article, two case studies with applications are presented.

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Closed form expression for the inverse cumulative distribution function of Nakagami distribution

Cited by 5 publications

References 37 publications

Efficient Concurrent Execution of Smart Contracts in Blockchain Sharding

Efficient Concurrent Execution of Smart Contracts in Blockchain Sharding

Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication

New Mathematical Approximations for the Cumulative Normal Distribution Function

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