Unit Nadarajah and Haghighi distribution: Properties and applications in quality control

Document Type : Research Article

Authors

1 Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan.

2 Department of Statistics, St. Anthony's College, Shillong, India.

10.24200/sci.2021.57302.5167

Abstract

In practice, the data related to rates and proportion may have excess of ones wherein the beta distribution does not  fit well. To deal with the inflation of ones, this article introduces unit Nadarajah and Haghighi distribution. Besides deriving statistical properties of the proposed distribution, several estimation methods are discussed. In particular, maximum likelihood estimation, least squares estimation, weighted least squares estimation, maximum product of spacing, minimum spacing absolute distance estimation, minimum spacing absolute log-distance estimation, Cramer-Von-Mises, Anderson-Darling method and right-tail Anderson-Darling method are considered. Using real data sets, it is shown that the new distribution outperforms some well-known existing distributions. Furthermore, the application of the proposed distribution in quality control is also discussed. A control chart using unit Nadarajah and Haghighi distribution is constructed and its performance is evaluated using the average run length.

Keywords

Main Subjects

References

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Scientia Iranica
Volume 32, Issue 8
Transactions on Industrial Engineering (E)
March and April 2025 Article ID:5167

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History

  • Receive Date: 08 December 2020
  • Revise Date: 12 September 2021
  • Accept Date: 15 November 2021

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