Document Type : Article


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

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


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.


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