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19 pages, 510 KiB

Open AccessArticle

A New Sine Family of Generalized Distributions: Statistical Inference with Applications

by SidAhmed Benchiha, Laxmi Prasad Sapkota, Aned Al Mutairi, Vijay Kumar, Rana H. Khashab, Ahmed M. Gemeay, Mohammed Elgarhy and Said G. Nassr

Math. Comput. Appl. 2023, 28(4), 83; https://doi.org/10.3390/mca28040083 - 16 Jul 2023

Cited by 21 | Viewed by 3231

Abstract

In this article, we extensively study a family of distributions using the trigonometric function. We add an extra parameter to the sine transformation family and name it the alpha-sine-G family of distributions. Some important functional forms and properties of the family are provided in a general form. A specific sub-model alpha-sine Weibull of this family is also introduced using the Weibull distribution as a parent distribution and studied deeply. The statistical properties of this new distribution are investigated and intended parameters are estimated using the maximum likelihood, maximum product of spacings, least square, weighted least square, and minimum distance methods. For further justification of these estimates, a simulation experiment is carried out. Two real data sets are analyzed to show the suggested model’s application. The suggested model performed well compares to some existing models considered in the study. Full article

(This article belongs to the Special Issue Statistical Inference in Linear Models)

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22 pages, 503 KiB

Open AccessArticle

Efficient Difference and Ratio-Type Imputation Methods under Ranked Set Sampling

by Shashi Bhushan, Anoop Kumar, Tolga Zaman and Aned Al Mutairi

Axioms 2023, 12(6), 558; https://doi.org/10.3390/axioms12060558 - 5 Jun 2023

Cited by 21 | Viewed by 1552

Abstract

It is well known that ranked set sampling (RSS) is more efficient than simple random sampling (SRS). Furthermore, the presence of missing data vitiates the conventional results. Only a minuscule amount of work has been conducted under RSS with missing data. This paper makes a modest attempt to provide some efficient difference- and ratio-type imputation methods in the presence of missing values under RSS. The envisaged imputation methods are demonstrated to provide better results than the existing imputation methods. The theoretical results are enhanced by a computational analysis using real and hypothetically generated symmetric (Normal) and asymmetric (Gamma and Weibull) populations. The computational results show that the proposed imputation method outperforms the existing imputation methods in terms of its higher percent relative efficiency. Additionally, the impact of skewness and kurtosis on the efficiency of the suggested imputation methods has also been calculated. Full article

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20 pages, 1791 KiB

Open AccessArticle

Optimal Plan of Multi-Stress–Strength Reliability Bayesian and Non-Bayesian Methods for the Alpha Power Exponential Model Using Progressive First Failure

by Ehab M. Almetwally, Refah Alotaibi, Aned Al Mutairi, Chanseok Park and Hoda Rezk

Symmetry 2022, 14(7), 1306; https://doi.org/10.3390/sym14071306 - 23 Jun 2022

Cited by 13 | Viewed by 2356

Abstract

It is extremely frequent for systems to fail in their demanding operating environments in many real-world contexts. When systems reach their lowest, highest, or both extreme operating conditions, they usually fail to perform their intended functions, which is something that researchers pay little attention to. The goal of this paper is to develop inference for multi-reliability using unit alpha power exponential distributions for stress–strength variables based on the progressive first failure. As a result, the problem of estimating the stress–strength function R, where X, Y, and Z come from three separate alpha power exponential distributions, is addressed in this paper. The conventional methods, such as maximum likelihood for point estimation, Bayesian and asymptotic confidence, boot-p, and boot-t methods for interval estimation, are also examined. Various confidence intervals have been obtained. Monte Carlo simulations and real-world application examples are used to evaluate and compare the performance of the various proposed estimators. Full article

(This article belongs to the Special Issue Symmetric Distributions, Moments and Applications)

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24 pages, 5902 KiB

Open AccessArticle

Optimal Design for a Bivariate Step-Stress Accelerated Life Test with Alpha Power Exponential Distribution Based on Type-I Progressive Censored Samples

by Refah Alotaibi, Aned Al Mutairi, Ehab M. Almetwally, Chanseok Park and Hoda Rezk

Symmetry 2022, 14(4), 830; https://doi.org/10.3390/sym14040830 - 16 Apr 2022

Cited by 14 | Viewed by 2603

Abstract

We consider an optimization design for the alpha power exponential (APE) distribution as asymmetrical probability distributions under progressive type-I censoring for a step-stress accelerated life test. In this study, two stress variables are taken into account. To save the time and cost of lifetime testing, progressive censoring and accelerated life testing are utilized. The test units’ lifespans are supposed to follow an APE distribution. A cumulative exposure model is used to study the impact of varying stress levels. A log-linear relationship between the APE distribution’s scale parameter and stress is postulated. The maximum likelihood estimators, Bayesian estimators of the model parameters based on the symmetric loss function, approximate confidence intervals (CIs) and credible intervals are provided. Under normal operating conditions, an ideal test plan is designed by minimizing the asymptotic variance of the percentile life. Full article

(This article belongs to the Section Mathematics)

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