Development of the convolutions of truncated normal random variables with three different quality characteristics in engineering applications

Krenek, Russell W.; Cha, Jinho; Cho, Byung Rae

doi:10.1016/j.cie.2015.12.014

Cited by 9 publications

(2 citation statements)

References 21 publications

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“…In statistics, there is a rule called the 68-95-99.7 rule to deal around the mean value in the normal distribution, sometimes known as the empirical rule [13,[27][28][29], in order to get more accurately, 68.27%, 95.45% and 99.73% of the random variables within one standard deviation, two standard deviations, and three standard deviations of the mean, respectively.…”

Section: Rules For Truncated Normal Pdf Datamentioning

confidence: 99%

Probabilistic Optimal Power Dispatch Considering Price-Based Real-Time Demand Response

Chhor¹,

Leeton²,

Chayakulkheeree³

2019

IJIES

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In this paper, a probabilistic optimal power dispatch (POPD) using linear programming (LP) is proposed for solving the power generation dispatch with price-based real-time demand response (PRDR). The expected shortterm load forecast is represented by a probabilistic distribution function. The simulation result has prosperously shown that the proposed method could handle the POPD solutions for real power dispatch considering PRDR by using probabilistic Truncated normal distribution function (PTNF). The PTNF is used in a vigorous part of the framework to eject the infeasible results during the computation. This would lead the results to the high degree of accuracy comparing to the normal sampling methods. The simulation results showed that the proposed method can efficiently and effectively minimize the total power generation cost while trading off the PRDR cost in the POPD problem with load uncertainty.

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Section: Rules For Truncated Normal Pdf Datamentioning

confidence: 99%

Probabilistic Optimal Power Dispatch Considering Price-Based Real-Time Demand Response

Chhor¹,

Leeton²,

Chayakulkheeree³

2019

IJIES

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“…In real life applications, various statistical distributions have been utilized to analyze datasets under investigation, among those we mention the wellknown Half-Normal (HN) distribution with zero mean. This truncated distribution has been used for risk analysis in several fields such as engineering (Krenek et al 2016), finance (Aharony et al 1980, Badia et al 2020, and medicine (Krause et al 2018). Despite being widely used, the HN distribution has a limited control on the shape of the produced models because it has a scale parameter only.…”

Section: Introductionmentioning

confidence: 99%

A Flexible Probability Model for Reliability Data Analysis: The Extended Half-Normal Distribution with Further Results

Khorsheed¹,

Salinas²,

Bakouch³

2022

KJS publishes peer-review articles in Mathematics, Computer Sci

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Recent years have shown growth in the potential applications of extensions of skew and half-normal distributions. In this paper, we provide and study, in detail, an extended class of such distributions. The presented distribution has a scale parameter and two shape parameters. The motivations behind the development of this distribution are: 1- the probability distribution function has skewed, unimodal and bathtub shapes with different styles and the hazard rate function is increasing with various shapes, which makes this distribution flexible enough to analyze reliability data; 2- it can be expressed as a mixture of the Generalized Half-Normal distribution and the new weighted Generalized Half-Normal distribution. A number of statistical results are derived. Monte Carlo simulation analysis is carried out with Maximum Likelihood Estimation to assess the performance of this technique for a variety of the distribution parameter values. The power of the distribution is demonstrated with real applications using two reliability datasets from the industry. The results reveal that the proposed distribution outperformed the Generalized Lindley, Exponentiated Exponential, Gamma, Alpha-Skew-Normal, the Half-Alpha- Skew-Normal, and the Modified Generalized Half-Normal distributions.

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Inference for a constant-stress model under progressive type-II censored data from the truncated normal distribution

Sief,

Liu,

Abd El-Raheem

2023

Comput Stat

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Development of the convolutions of truncated normal random variables with three different quality characteristics in engineering applications

Cited by 9 publications

References 21 publications

Probabilistic Optimal Power Dispatch Considering Price-Based Real-Time Demand Response

Probabilistic Optimal Power Dispatch Considering Price-Based Real-Time Demand Response

A Flexible Probability Model for Reliability Data Analysis: The Extended Half-Normal Distribution with Further Results

Inference for a constant-stress model under progressive type-II censored data from the truncated normal distribution

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