A numerical computing for the CDF of injective RVT with optimization analysis using Weibull distribution: Applications to stochastic heat transfer Abdelhafeez Elshekhipy, Manal Alohali, Nawal Almalki, Aisha Alwehebi, Noha Almulla, Saad M. Almuaddi, Zainab Alsoufi, Mohamed S.M. Bahgat Alexandria Engineering Journal, 2025 This paper presents a novel numerical method for computing the cumulative distribution function (CDF) of one-to-one univariate Random Variable Transformations (RVTs). This method is crucial for assessing the statistical representation weight of random changes within the RVT domain, offering a practical alternative to traditional analytical methods, which are often limited in applicability. The research outlines the challenges posed by the analytical computation of the CDF for one-to-one RVTs, motivating the development of a more accessible numerical approach. This approach first verifies if the RVT function is one-to-one, then uses the bisection method to approximate its inverse of RVT function, enabling numerical evaluation of the CDF of RVT based on a governing model. The procedures are algorithmically detailed to facilitate the computational implementation. Additionally, an analytical re-evaluation generates an optimal fitted path for the numerical behavior of the CDF of RVT, using the Weibull distribution model to provide a mathematical model simulating the RVT's statistical characteristics approximately. The methodology is applied to compute the probabilistic distribution of uncertain thermal properties generated from solving a stochastic heat transfer problem, due to analyzing random variations in thermal diffusivity with a Gamma distribution as a case study to address potential measurement errors.
Point and Interval Estimators of R = P[Y < X ] Based on Gompertz Distribution and Ranked Set Sampling Data Thailand Statistician, 2021
Estimation of reliability in a multicomponent stress- strength model based on generalized linear failure rate distribution M. KH. Hassan, M. I. Alohali Hacettepe Journal of Mathematics and Statistics, 2018 In this paper, we consider the problem of estimation reliability in multicomponent stress-strength model, when the system consists of $k$-components have strength are given by independently and identically distributed random variables $X_{1},...,X_{k}$ each component experiencing a random stress governed by a random variable $Y$. The reliability such system is obtained when strength and stress variables are given by a generalized linear failure rate distribution. The system is regarded as alive only if at least $s$ out of $k$ $(s<k)$ strength exceed the stress. The multicomponent reliability of the system is given by $R_{s,k}=P[$ at least $s$ of $X_{1},...,X_{k}$ exceed $Y]$. The maximum likelihood estimator $(MLE)$ and Bayes estimator of $R_{s,k}$ are obtained. A simulation study is performed to compare the different estimators of $R_{s,k}$. Real data is used as a practical application of the proposed procedure.
RECENT SCHOLAR PUBLICATIONS
A numerical computing for the CDF of injective RVT with optimization analysis using Weibull distribution: Applications to stochastic heat transfer A Elshekhipy, M Alohali, N Almalki, A Alwehebi, N Almulla, SM Almuaddi, ... Alexandria Engineering Journal 122, 665-680 , 2025 2025.0
Statistical comparison of models and machine learning for predicting Arrhenius parameters in ternary liquid mixtures E Mliki, R Hamdi, S Jaffali, M Al-Ohali Journal of Molecular Liquids 421, 126933 , 2025 2025.0
Cultivating Calculus Excellence: Smart Learning and Peer Tutoring for Math Empowerment in Female Science College Students EA Alibraheim, NH Youssef, OH Helal, MI AlOhali, SM Almuaddi, ... Migration Letters 21 (S1), 379-395 , 2024 2024.0
Peer Flipped Learning in Financial Mathematics: Enhancing Academic Achievement and Mathematical Thinking in College of Science Students NH Youssef, EA Alibraheim, OH Helal, MI AlOhali Migration Letters 20 (S2), 850-870 , 2023 2023.0
A new application of R = P [ Y < X ] for the inverse Lindley distribution using ranked set sampling MK Hassan, MI Alohali, FA Alojail Journal of Statistics and Management Systems 24 (8), 1713-1731 , 2021 2021.0 Citations: 7
Point and Interval Estimators of R= P [Y< X] Based on Gompertz Distribution and Ranked Set Sampling Data MK Hassan, MI Alohali, FA Alojail Thailand Statistician 19 (4), 784-796 , 2021 2021.0 Citations: 3
Validation of Messaâdi equation on viscosity-temperature dependence for some ternary liquid mixtures by statistical correlation analysis DH Alotaibi, E Mliki, N Vrinceanu, TK Srinivasa, ME Al-Ohali, AA Al-Arfaj, ... Physics and Chemistry of Liquids 58 (5), 590-602 , 2020 2020.0 Citations: 9
Estimation of reliability in a multicomponent stress-strength model based on generalized linear failure rate distribution MK Hassan, MI Alohali Hacettepe Journal of Mathematics and Statistics 47 (6), 1634-1651 , 2018 2018.0 Citations: 18
Estimating the Completion time of Stochastic Activity networks with uniform distributed activity Times Archives Des Sciences Journal Vol 66 (4): 115-134 YH Abdelkader, M Al-Ohali 2013.0 Citations: 3
Reliability equivalence factors in exponentiated exponential distribution MAO Abdelkader, Y. H., A. I. Shawky Wulfenia journal 20 (3), 75-85 , 2013 2013.0 Citations: 15
Estimating the Completion time of Stochastic Activity networks with uniform distributed activity Times MAO Abdelkader, Yousry H. Archives Des Sciences 66 (4) , 2013 2013.0 Citations: 6
Reliability Equivalence of Independent Non-identical Parallel and Series Systems MIAO Y.H.Abdelkader, A.I .Shawky Life Science Journal 9 (3), 577-583 , 2012 2012.0 Citations: 4
Prediction in the Presence of Outliers and Random Sample Size from the Pareto Model AASME Al-Ohaly Proc. Of the Saudi Science Conference . KFUPM, 439-455 , 2001 2001.0
Bayes 2-sample prediction for the Pareto distribution MEAO Ahmed A. Soliman Journal of the Egyptian Mathematical Society 8 (1) , 2000 2000.0 Citations: 4
The Impact of Integrating the Flipped Classroom Strategy with Think-Aloud Techniques in Mathematics Instruction on Enhancing Deep Understanding and Self-Efficacy Among Female … OH Helal, EA Alibraheim, NH Youssef, MM Aljohani, MI AlOhali, ...
MOST CITED SCHOLAR PUBLICATIONS
Estimation of reliability in a multicomponent stress-strength model based on generalized linear failure rate distribution MK Hassan, MI Alohali Hacettepe Journal of Mathematics and Statistics 47 (6), 1634-1651 , 2018 2018.0 Citations: 18
Reliability equivalence factors in exponentiated exponential distribution MAO Abdelkader, Y. H., A. I. Shawky Wulfenia journal 20 (3), 75-85 , 2013 2013.0 Citations: 15
Validation of Messaâdi equation on viscosity-temperature dependence for some ternary liquid mixtures by statistical correlation analysis DH Alotaibi, E Mliki, N Vrinceanu, TK Srinivasa, ME Al-Ohali, AA Al-Arfaj, ... Physics and Chemistry of Liquids 58 (5), 590-602 , 2020 2020.0 Citations: 9
A new application of R = P [ Y < X ] for the inverse Lindley distribution using ranked set sampling MK Hassan, MI Alohali, FA Alojail Journal of Statistics and Management Systems 24 (8), 1713-1731 , 2021 2021.0 Citations: 7
Estimating the Completion time of Stochastic Activity networks with uniform distributed activity Times MAO Abdelkader, Yousry H. Archives Des Sciences 66 (4) , 2013 2013.0 Citations: 6
Reliability Equivalence of Independent Non-identical Parallel and Series Systems MIAO Y.H.Abdelkader, A.I .Shawky Life Science Journal 9 (3), 577-583 , 2012 2012.0 Citations: 4
Bayes 2-sample prediction for the Pareto distribution MEAO Ahmed A. Soliman Journal of the Egyptian Mathematical Society 8 (1) , 2000 2000.0 Citations: 4
Point and Interval Estimators of R= P [Y< X] Based on Gompertz Distribution and Ranked Set Sampling Data MK Hassan, MI Alohali, FA Alojail Thailand Statistician 19 (4), 784-796 , 2021 2021.0 Citations: 3
Estimating the Completion time of Stochastic Activity networks with uniform distributed activity Times Archives Des Sciences Journal Vol 66 (4): 115-134 YH Abdelkader, M Al-Ohali 2013.0 Citations: 3
A numerical computing for the CDF of injective RVT with optimization analysis using Weibull distribution: Applications to stochastic heat transfer A Elshekhipy, M Alohali, N Almalki, A Alwehebi, N Almulla, SM Almuaddi, ... Alexandria Engineering Journal 122, 665-680 , 2025 2025.0
Statistical comparison of models and machine learning for predicting Arrhenius parameters in ternary liquid mixtures E Mliki, R Hamdi, S Jaffali, M Al-Ohali Journal of Molecular Liquids 421, 126933 , 2025 2025.0
Cultivating Calculus Excellence: Smart Learning and Peer Tutoring for Math Empowerment in Female Science College Students EA Alibraheim, NH Youssef, OH Helal, MI AlOhali, SM Almuaddi, ... Migration Letters 21 (S1), 379-395 , 2024 2024.0
Peer Flipped Learning in Financial Mathematics: Enhancing Academic Achievement and Mathematical Thinking in College of Science Students NH Youssef, EA Alibraheim, OH Helal, MI AlOhali Migration Letters 20 (S2), 850-870 , 2023 2023.0
Prediction in the Presence of Outliers and Random Sample Size from the Pareto Model AASME Al-Ohaly Proc. Of the Saudi Science Conference . KFUPM, 439-455 , 2001 2001.0
The Impact of Integrating the Flipped Classroom Strategy with Think-Aloud Techniques in Mathematics Instruction on Enhancing Deep Understanding and Self-Efficacy Among Female … OH Helal, EA Alibraheim, NH Youssef, MM Aljohani, MI AlOhali, ...
