Article
Multidisciplinary Sciences
Abdulhakim A. Al-Babtain, Devendra Kumar, Ahmed M. Gemeay, Sanku Dey, Ahmed Z. Afify
Summary: This paper introduces a new distribution WMOPL to model engineering related data, which shows better performance and flexibility compared to some well-known extensions of the Power-Lindley and Lindley distributions. Seven estimation methods are considered to estimate WMOPL parameters, and a simulation study is conducted to evaluate their performance. The study demonstrates the superior performance and flexibility of the introduced distribution through real data application.
JOURNAL OF KING SAUD UNIVERSITY SCIENCE
(2021)
Article
Multidisciplinary Sciences
Abdul Rahman Othman, Lai Choo Heng, Sonia Aissa, Nora Muda
Summary: Three methods for approximating the sum of lognormal variates to a lognormal distribution were studied: the Wilkinson approximation, the Monte Carlo version of the Wilkinson approximation, and the approximation using estimated maximum likelihood lognormal parameters. Lognormal variates were empirically generated using Monte Carlo simulation under various conditions. The evaluation of these approximation methods was conducted using the Anderson Darling test. Results demonstrated that the approximation using estimated maximum likelihood lognormal parameters yielded Type I errors close to the desired target of 0.05 and was considered the best approximation.
Article
Mathematical & Computational Biology
Nicholas Devogel, Paul L. Auer, Regina Manansala, Tao Wang
Summary: This study examines the asymptotic distributions of the likelihood ratio test (LRT), the restricted likelihood ratio test (RLRT), the F test, and the sequence kernel association test (SKAT) statistics for testing an additive effect of expected familial relatedness (FR) in a linear mixed model. The covariance structure for modeling the FR effect in a LMM is presented, and the eigenvalues for the log-likelihood and restricted log-likelihood are established under replicate family settings. The asymptotic null distributions of the test statistics under more general replicate family settings (GRFS) are derived, and a power comparison of these test statistics is made via simulation.
STATISTICS IN MEDICINE
(2023)
Article
Computer Science, Artificial Intelligence
Badr Alnssyan, Ekramy A. Hussein, Morad Alizadeh, Ahmed Z. Afify, Ashraf D. Abdellatif
Summary: We propose a new wider family called the weighted Lindley-G family and study its mathematical properties and special sub-models. We explore the estimation of model parameters using eight different approaches and compare their performance through detailed simulations, providing a guideline for selecting the best approach. Two real-life data applications demonstrate the potential of the new family, showing its greater flexibility compared to commonly cited families in distribution theory literature such as the exponentiated-G, beta-G, transmuted-G, and alpha-power-G families under the same baseline model.
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
(2023)
Article
Multidisciplinary Sciences
Najwan Alsadat, Amal S. Hassan, Mohammed Elgarhy, Christophe Chesneau, Rokaya Elmorsy Mohamed
Summary: This paper considers the estimation of stress-strength reliability when the stress and strength variables follow unit Gompertz distributions with similar scale parameters. The unit Gompertz distribution is chosen due to its symmetric and asymmetric properties that can accommodate various data shapes. The reliability estimate is determined using seven frequentist techniques based on ranked set sampling and simple random sampling. A simulation study is conducted to evaluate the effectiveness of the recommended ranked set sampling-based estimates. The results show that the reliability estimates from the maximum product spacing approach are the lowest compared to other methods. Additionally, the ranked set sampling-based estimates outperform those obtained from a comparable simple random sampling approach. Two real data sets reflecting the survival periods of head and neck cancer patients are also analyzed.
Article
Engineering, Industrial
Anh Tuan Bui, Daniel W. Apley
Summary: This article introduces the spc4sts package, the first implementation to address SPC problems for STS data. The package provides tools for modeling, monitoring for defects and changes, and diagnosing variation and other patterns or modes that occur due to manufacturing and processing conditions.
JOURNAL OF QUALITY TECHNOLOGY
(2021)
Article
Mathematics
Anum Shafiq, Tabassum Naz Sindhu, Sanku Dey, Showkat Ahmad Lone, Tahani A. A. Abushal
Summary: In this study, a new three-parameter lifetime model, named the half-logistic unit Gompertz type-I distribution, is proposed by combining the type-I half-logistic G family and the unit-Gompertz model. The novel model adds a new tuning parameter to make the unit-Gompertz model more flexible. Diagrams and numerical results are used to analyze the mathematical and statistical aspects of the new model. The efficiency of distribution parameter estimation is evaluated using various classical methodologies.
Article
Mathematics
Karol Santoro, Hector J. Gomez, Diego Gallardo, Inmaculada Barranco-Chamorro, Hector W. Gomez
Summary: A new class of densities for modelling non-negative data is introduced, which is based on the skew-symmetric family of distributions proposed by Azzalini. The study focuses on the model generated by the skew-normal distribution, called the Extended Half Skew-Normal distribution, and examines its relevant properties. The parameters are estimated using moment and maximum likelihood methods, and the performance of the maximum likelihood estimators is evaluated through simulation studies. Two real applications are included, demonstrating that the EHSN provides a better fit compared to other methods in the literature.
Article
Multidisciplinary Sciences
Abdulhakim A. Al-Babtain, Ibrahim Elbatal, Hazem Al-Mofleh, Ahmed M. Gemeay, Ahmed Z. Afify, Abdullah M. Sarg
Summary: This paper introduces a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to enhance the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated, with a detailed study on the TBX-exponential distribution. Eight estimation approaches for the TBX-exponential parameters are discussed and recommendations are made based on numerical simulations.Illustrations are provided using skewed real data sets from engineering sciences to demonstrate the importance and flexibility of the TBX-exponential model compared to other existing competing distributions.
Article
Statistics & Probability
Mohammad Anas, Aijaz Ahmad Dar, Aquil Ahmed, Mohd Arshad
Summary: The author introduces a generalization of well-known probability distributions using weighted probability distributions and names it the Kth-order equilibrium Weibull distribution (KEWD). Various properties of KEWD are studied, including its hazard rate and belonging to the log exponential family. The ordering relations of KEWD are compared to the baseline model, Weibull distribution. Parameters are estimated using maximum likelihood estimation technique, and a simulation study is conducted to analyze the asymptotic normality behavior of the estimators.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2023)
Article
Mathematics
Juan Duarte, Guillermo Martinez-Florez, Diego Ignacio Gallardo, Osvaldo Venegas, Hector W. Gomez
Summary: This article presents a novel bimodal model based on the epsilon-skew-normal distribution. The model generates bimodal distributions similar to the mixture of normal distributions. The study explores the properties of this new family, applies maximum likelihood estimators, calculates the information matrix, and conducts simulations to assess parameter recovery. The results are illustrated using three real data sets, suggesting the potential use of this new distribution for modeling bimodal data.
Article
Computer Science, Interdisciplinary Applications
Ringo Thomas Tchouya, Stefano Nasini, Sophie Dabo-Niang
Summary: This paper presents a numerical estimation procedure for the influential-imitator diffusion, and proposes a maximum likelihood approach for the estimation of the model parameters. The paper also develops a truncated series expansion for increased accuracy in the estimation. Empirical and computational tests are conducted using a dataset on cannabis consumption among secondary school students in Glasgow, confirming the hypothesis on peer influences.
COMPUTERS & OPERATIONS RESEARCH
(2023)
Article
Statistics & Probability
Jesse Goodman
Summary: This paper provides an approximation to the density of a random variable using the saddlepoint approximation method, and proves the basic result of the approximation error between the saddlepoint MLE and the true MLE. The approximation errors are asymptotically negligible compared to the inferential uncertainty in all cases.
ANNALS OF STATISTICS
(2022)
Article
Automation & Control Systems
Manuel Galea, Mario de Castro
Summary: This paper deals with the inference of structural parameters in a heteroscedastic functional measurement error model under the assumption of normal distribution. The conditional maximum likelihood (CML) approach is used, and it is shown that the CML estimators have explicit expressions and exact sampling distributions. Additionally, it is demonstrated that the classical test statistics for testing hypotheses have exact distributions. The statistical inference tools developed in this paper are applied to a data set comparing measurement methods.
CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS
(2023)
Article
Mathematics, Applied
Aurora Monter-Pozos, Elizabeth Gonzalez-Estrada
Summary: The skew normal distribution is a flexible and applicable distribution for modeling symmetric and skew data sets. This paper proposes a method based on data transformation to test the hypothesis that a sample follows a skew normal distribution, and provides formulas for calculating critical values. The analysis of real data sets demonstrates the plausibility of the skew normal distribution in modeling the behavior of real data.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Statistics & Probability
Thaddeus Tarpey, Nicola Loperfido
JOURNAL OF MULTIVARIATE ANALYSIS
(2015)
Article
Mathematics, Applied
Nicola Loperfido
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(2015)
Article
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Nicola Loperfido
STATISTICS & PROBABILITY LETTERS
(2015)
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Statistics & Probability
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STATISTICS & PROBABILITY LETTERS
(2010)
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STATISTICS & PROBABILITY LETTERS
(2013)
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Nicola Loperfido
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Business, Finance
Christopher Adcock, Martin Eling, Nicola Loperfido
EUROPEAN JOURNAL OF FINANCE
(2015)
Article
Business, Finance
Giovanni De Luca, Nicola Loperfido
EUROPEAN JOURNAL OF FINANCE
(2015)
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Statistics & Probability
Marcus C. Christiansen, Nicola Loperfido
JOURNAL OF APPLIED PROBABILITY
(2014)
