Open Access

ARTICLE

Zubair Lomax Distribution: Properties and Estimation Based on Ranked Set Sampling

Rashad Bantan¹, Amal S. Hassan², Mahmoud Elsehetry^{3, *}

1 Deanship of Scientific Research, King AbdulAziz University, Jeddah, 21589, Saudi Arabia.
2 Faculty of Graduate Studies for Statistical Research, Cairo University, Cairo, 11865, Egypt.
3 Deanship of Information Technology, King AbdulAziz University, Jeddah, 21589, Saudi Arabia.

* Corresponding Author: Mahmoud Elsehetry. Email: .

Computers, Materials & Continua 2020, 65(3), 2169-2187. https://doi.org/10.32604/cmc.2020.011497

Received 11 May 2020; Accepted 25 June 2020; Issue published 16 September 2020

Abstract

In this article, we offer a new adapted model with three parameters, called Zubair Lomax distribution. The new model can be very useful in analyzing and modeling real data and provides better fits than some others new models. Primary properties of the Zubair Lomax model are determined by moments, probability weighted moments, Renyi entropy, quantile function and stochastic ordering, among others. Maximum likelihood method is used to estimate the population parameters, owing to simple random sample and ranked set sampling schemes. The behavior of the maximum likelihood estimates for the model parameters is studied using Monte Carlo simulation. Criteria measures including biases, mean square errors and relative efficiencies are used to compare estimates. Regarding the simulation study, we observe that the estimates based on ranked set sampling are more efficient compared to the estimates based on simple random sample. The importance and flexibility of Zubair Lomax are validated empirically in modeling two types of lifetime data.

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Citations