Far East Journal of Theoretical Statistics © 2016 Pushpa Publishing House, Allahabad, India Published Online: March 2016 http://dx.doi.org/10.17654/TS052010001 Volume 52, Number 1, 2016, Pages 1-15 ISSN: 0972-0863 Received: June 7, 2015; Revised: July 9, 2015; Accepted: July 25, 2015 2010 Mathematics Subject Classification: 62F10. Keywords and phrases: beta function, digamma function, gamma function, inverse Weibull distribution, method of maximum likelihood, method of product spacings, Newton-Raphson method, trigamma function. Communicated by Jinyu Li; Editor: Advances and Applications in Statistics: Published by Pushpa Publishing House. METHOD OF PRODUCT SPACINGS PARAMETER ESTIMATION FOR BETA INVERSE WEIBULL DISTRIBUTION Mezbahur Rahman, Dayeong An and Mohammad Shaha Alam Patwary Department of Mathematics and Statistics Minnesota State University Mankato, MN 56001, U. S. A. e-mail: mezbahur.rahman@mnsu.edu dayeong.an@mnsu.edu mohammad-shaha.patwary@mnsu.edu Abstract The inverse Weibull distribution is one of the widely applied distributions. In this paper, we are going to extend the study of the beta inverse Weibull distribution (BIW). The BIW with three parameters is analyzed by using the method of product spacing (MPS) and compared with the maximum likelihood estimate (MLE). To estimate the model parameters, Newton-Raphson method is applied and the table of simulation results is shown. Finally, practical use of the model is demonstrated by dint of an application to real data. For the real data computation, the estimate of the variance-covariance matrix and the estimates are provided.