Sabir Ali Siddiqui, Shradha Dwivedi,
Peeyush Dwivedi, Irfan Siddiqui
Department of Mathematics and Sciences
CAAS, Dhofar University
Salalah, SULTANATE OF OMAN
Mathematics Unit
FP, Dhofar University
Salalah, SULTANATE OF OMAN
Department of Business Studies
College of Technology
Salalah, SULTANATE OF OMAN
Department of Management Studies
Sinhagad College of Engineering
Pune, INDIA

Abstract. In the present article, we derived a new Size-biased distribution from Mukherjee-Islam distribution. Flexibility of the model is derived by its moments, moment generating function (mgf) and characteristic function. Other important properties like Fisher's information matrix and Shannon's entropy are also derived which gives the measure of uncertainty in the system. Maximum likelihood estimator (MLE) and Baye's estimator of size-biased distribution are obtained and in the last, test of size biasedness is done.

Received: March 7, 2016

AMS Subject Classification:

Key Words and Phrases: Mukherjee-Islam distribution, size-biased Mukherjee-Islam Distribution (SBMID), Shannon's entropy, Fisher's information matrix, non-informative priors

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