A Flexible Form for the Topp-Leone Distribution: Properties and Different Methods of Estimation

Hiba  Z. Muhammed; El-Sayed  A. El-Sherpieny; Amira  Hassan EL-Sayed

Authors

Hiba Z. Muhammed Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
El-Sayed A. El-Sherpieny Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
Amira Hassan EL-Sayed Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt

Keywords:

Maximum likelihood estimation, maximum product spacing estimation, least square estimation, Bayesian estimation, MCMC, censored Type-II

Abstract

It is important to find new simple explicit forms for distributions instead of their old implicit forms which cause some problems in mathematical properties and generating random numbers. In this paper, a simple transformation is applied to the Topp-Leone distribution giving a new distribution called the flexible Toppe-Leone distribution having more flexibility in mathematical properties and simulation studies specially generating random numbers. Some different methods of estimation are used for the flexible Toppe-Leone distribution via classical and Bayesian approaches using a progressive Type-II censoring scheme, a simulation study is performed to compare estimators' behaviors of the estimation methods.

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