UNIT NADARAJAH AND HAGHIGHI DISTRIBUTION: PROPERTIES AND APPLICATIONS IN QUALITY CONTROL

Document Type : Article

Authors

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

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

Abstract

This article introduces unit Nadarajah and Haghighi distribution to deal with the inflation of ones. Besides deriving statistical properties of the proposed distribution, several estimation methods are discussed. In particular, maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squared estimation (WLSE), maximum product spacing (MPS), minimum spacing absolute distance estimation (MSADE), minimum spacing absolute log-distance estimation (MSALDE), Cram'er-Von-Mises (CVM), Anderson-Darling method (AD) and right-tail Anderson-Darling method (RAD) are considered. Using real data sets, it is shown that the new distribution outperforms some well-known existing distribution. 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


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Articles in Press, Accepted Manuscript
Available Online from 14 November 2021
  • Receive Date: 08 December 2020
  • Revise Date: 12 September 2021
  • Accept Date: 14 November 2021