Topp–Leone Linear Exponential Distribution

Bol A. M. Atem; Suleman Nasiru; Kwara Nantomah

doi:10.1515/eqc-2017-0022

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Article

Topp–Leone Linear Exponential Distribution

Bol A. M. Atem , Suleman Nasiru and Kwara Nantomah

Published/Copyright: January 18, 2018

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From the journal Stochastics and Quality Control Volume 33 Issue 1

Abstract

This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

Keywords: Topp–Leone; Linear Exponential; Bivariate; Quantile; Moment

MSC 2010: 62E15; 60E05

A Appendix

The following are the elements of the observed information matrix:

∂2⁡ℓ∂⁡α2=-nα2,

∂2⁡ℓ∂⁡α⁢∂⁡θ=∑i=1n(2⁢xi⁢e-2⁢(β⁢xi22+θ⁢xi)1-e-2⁢(β⁢xi22+θ⁢xi)),

∂2⁡ℓ∂⁡α⁢∂⁡β=∑i=1n(xi2⁢e-2⁢(β⁢xi22+θ⁢xi)1-e-2⁢(β⁢xi22+θ⁢xi)),

∂2⁡ℓ∂⁡θ2=∑i=1n(-1(θ+β⁢xi)2)+(α-1)⁢∑i=1n[-(4⁢xi2⁢e-2⁢(β⁢xi22+θ⁢xi)(1-e-2⁢(β⁢xi22+θ⁢xi))2)-(4⁢xi2⁢e-2⁢(β⁢xi22+θ⁢xi)1-e-2⁢(β⁢xi22+θ⁢xi))],

∂2⁡ℓ∂⁡θ⁢∂⁡β=∑i=1n(-xi(θ+β⁢xi)2)+(α-1)⁢∑i=1n[-(2⁢xi3⁢e-2⁢(β⁢xi22+θ⁢xi)(1-e-2⁢(β⁢xi22+θ⁢xi))2)-(2⁢xi3⁢e-2⁢(β⁢xi22+θ⁢xi)1-e-2⁢(β⁢xi22+θ⁢xi))],

∂2⁡ℓ∂⁡β2=∑i=1n(-xi2(θ+β⁢xi)2)+(α-1)⁢∑i=1n[-(xi4⁢e-2⁢(β⁢xi22+θ⁢xi)(1-e-2⁢(β⁢xi22+θ⁢xi))2)-(xi4⁢e-2⁢(β⁢xi22+θ⁢xi)1-e-2⁢(β⁢xi22+θ⁢xi))].

Competing Interests:

The authors declare that there is no conflict of interest regarding the publications of this article.

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Received: 2017-9-21

Revised: 2018-1-3

Accepted: 2018-1-4

Published Online: 2018-1-18

Published in Print: 2018-6-1

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Articles in the same Issue

https://doi.org/10.1515/eqc-2017-0022

Keywords for this article

Topp–Leone; Linear Exponential; Bivariate; Quantile; Moment