A New 3-Parameter Bounded Beta Distribution: Properties, Estimation, and Applications

Althubyani, Faiza A.; El-Bar, Ahmed M. T. Abd; Fawzy, Mohamad A.; Gemeay, Ahmed M.

doi:10.3390/axioms11100504

Cited by 9 publications

(5 citation statements)

References 15 publications

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“…The Beta distribution is a versatile statistical distribution used to model random variables, and the PDF of a Beta distribution is given by [36]:…”

Section: Discussionmentioning

confidence: 99%

A Novel Statistical Framework for Optimal Sizing of Grid-Connected Photovoltaic–Battery Systems for Peak Demand Reduction to Flatten Daily Load Profiles

Nematirad,

Pahwa,

Natarajan

2024

Solar

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Integrating photovoltaic (PV) systems plays a pivotal role in the global shift toward renewable energy, offering significant environmental benefits. However, the PV installation should provide financial benefits for the utilities. Considering that the utility companies often incur costs for both energy and peak demand, PV installations should aim to reduce both energy and peak demand charges. Although PV systems can reduce energy needs during the day, their effectiveness in reducing peak demand, particularly in the early morning and late evening, is limited, as PV generation is zero or negligible at those times. To address this limitation, battery storage systems are utilized for storing energy during off-peak hours and releasing it during peak times. However, finding the optimal size of PV and the accompanying battery remains a challenge. While valuable optimization models have been developed to determine the optimal size of PV–battery systems, a certain gap remains where peak demand reduction has not been sufficiently addressed in the optimization process. Recognizing this gap, this study proposes a novel statistical model to optimize PV–battery system size for peak demand reduction. The model aims to flatten 95% of daily peak demands up to a certain demand threshold, ensuring consistent energy supply and financial benefit for utility companies. A straightforward and effective search methodology is employed to determine the optimal system sizes. Additionally, the model’s effectiveness is rigorously tested through a modified Monte Carlo simulation coupled with time series clustering to generate various scenarios to assess performance under different conditions. The results indicate that the optimal PV–battery system successfully flattens 95% of daily peak demand with a selected threshold of 2000 kW, yielding a financial benefit of USD 812,648 over 20 years.

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“…The Beta distribution is a versatile statistical distribution used to model random variables, and the PDF of a Beta distribution is given by [36]:…”

Section: Discussionmentioning

confidence: 99%

A Novel Statistical Framework for Optimal Sizing of Grid-Connected Photovoltaic–Battery Systems for Peak Demand Reduction to Flatten Daily Load Profiles

Nematirad,

Pahwa,

Natarajan

2024

Solar

View full text Add to dashboard Cite

show abstract

“…The Beta distribution is a versatile statistical distribution used to model random variables and the PDF of a Beta distribution is given by [34]:…”

Section: Discussionmentioning

confidence: 99%

A Novel Statistical Framework for Optimal Sizing of Grid-Connected Photovoltaic-Battery Systems for Peak Demand Reduction to Flatten Daily Load Profiles

Nematirad,

Pahwa,

Natarajan

2024

Preprint

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Integrating photovoltaic (PV) systems plays a pivotal role in the global shift toward renewable energy, offering significant environmental benefits. In many instances, utility companies pay for both energy and peak demand. PV systems can effectively reduce energy consumption during their operational periods, while, their contribution during peak hours, particularly in the early morning and late evening, is often limited. To address this issue, battery storage systems are utilized for storing energy during off-peak hours and releasing it during peak times. However, finding the optimal size of PV-battery systems remains a challenge. This study proposes a novel statistical model to optimize PV-battery system sizing for enhanced peak demand reduction. The model aims to flatten 95% of peak demand days up to a certain demand threshold, ensuring consistent energy supply and financial benefit for utility companies. A straightforward and effective search methodology is employed to determine the optimal system sizes. Additionally, the model effectiveness is rigorously tested through a modified Monte Carlo simulation coupled with time series clustering to generate various scenarios to assess performance under different conditions. The results indicate that the optimal PV-battery system successfully flattens 95% of daily peak demand up to 2000 kW, yielding a financial benefit of $812,648 over 20 years.

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“…Te E-Bayesian estimator for ϑ based on WLINEXLF with π 1 (φ, ϕ) can be obtained by solving equations ( 17), (21), and (22) as follows:…”

Section: E-bayesian Estimation For ϑ Under Wlinexlfmentioning

confidence: 99%

“…More recently, a three-parameter bounded beta distribution was a new model introduced by Althubyani et al [22] and MLE and Bayesian estimation under LINEXLF and squared error were used to estimate the distribution's unknown parameters. Atchadé et al [23] estimated the unknown parameters of the new power Topp-Leone generated distribution using MLE.…”

Section: Introductionmentioning

confidence: 99%

Bayesian and E-Bayesian Estimation for the Generalized Rayleigh Distribution under Different Forms of Loss Functions with Real Data Application

Eldemery,

Abd-Elfattah,

Mahfouz

et al. 2023

Journal of Mathematics

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This paper investigates the estimation of an unknown shape parameter of the generalized Rayleigh distribution using Bayesian and expected Bayesian estimation techniques based on type-II censoring data. Subsequently, these estimators are obtained using four different loss functions: the linear exponential loss function, the weighted linear exponential loss function, the compound linear exponential loss function, and the weighted compound linear exponential loss function. The weighted compound linear exponential loss function is a novel suggested loss function generated by combining weights with the compound linear exponential loss function. We use the gamma distribution as a prior distribution. In addition, the expected Bayesian estimator is obtained through three different prior distributions of the hyperparameters. Moreover, depending on the four distinct forms of loss functions, Bayesian and expected Bayesian estimation techniques are performed using Monte Carlo simulations to verify the effectiveness of the suggested loss function and to compare Bayesian and expected Bayesian estimation methods. Furthermore, the simulation results indicate that, depending on the minimum mean squared error, the Bayesian and expected Bayesian estimations corresponding to the weighted compound linear exponential loss function suggested in this paper have significantly better performance compared to other loss functions, and the expected Bayesian estimator also performs better than the Bayesian estimator. Finally, the proposed techniques are demonstrated using a set of real data from the medical field to clarify the applicability of the suggested estimators to real phenomena and to show that the discussed weighted compound linear exponential loss function is efficient and can be applied in a real-life scenario.

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A New 3-Parameter Bounded Beta Distribution: Properties, Estimation, and Applications

Cited by 9 publications

References 15 publications

A Novel Statistical Framework for Optimal Sizing of Grid-Connected Photovoltaic–Battery Systems for Peak Demand Reduction to Flatten Daily Load Profiles

A Novel Statistical Framework for Optimal Sizing of Grid-Connected Photovoltaic–Battery Systems for Peak Demand Reduction to Flatten Daily Load Profiles

A Novel Statistical Framework for Optimal Sizing of Grid-Connected Photovoltaic-Battery Systems for Peak Demand Reduction to Flatten Daily Load Profiles

Bayesian and E-Bayesian Estimation for the Generalized Rayleigh Distribution under Different Forms of Loss Functions with Real Data Application

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