A study on the estimation of the Transmuted Generalized Uniform Distribution

Issa Cherif Geraldo¹

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.1 , pp.33-39, Feb-2020

Online published on Feb 28, 2020

Copyright © Issa Cherif Geraldo . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

Abstract :
In this paper, we consider the maximum likelihood (ML) estimation of the parameters a new probability distribution recently developed and called transmuted generalized uniform distribution (TGUD). Because of the complicated form of its log-likelihood function, this ML estimation can only be done by using numerical optimization algorithms but this problem has not been studied yet. We address this lack through a comprehensive simulation study in R software using some of the best optimization algorithms (Newton, quasi-Newton and Nelder-Mead algorithms). It is found that the Nelder-Mead algorithm is the best of all the selected algorithms.

Key-Words / Index Term :
Numerical optimization, iterative method, maximum likelihood, parameter estimation, transmuted distribution

References :
[1] Z. Ahmad, G.G. Hamedani, N.S. Butt, “Recent developments in distribution theory: a brief survey and some new generalized classes of distributions”, Pakistan Journal of Statistics and Operations Research, Vol. 15, Issue 1, pp. 87–110, 2019.
[2] C. Subramanian, A.A. Rather, “Transmuted generalized uniform distribution”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 5, pp. 25-32, 2018.
[3] C.-S. Lee, “Estimations in a generalized uniform distribution”, Journal of the Korean Data and Information Science Society, Vol. 11, Issue 2, pp. 319–325, 2000.
[4] R Core Team, “R: A Language and Environment for Statistical Computing”, R Foundation for Statistical Computing, Austria, 2019.
[5] I. Griva, S.G. Nash, A. Sofer, “Linear and Nonlinear Optimization”, Society for Industrial and Applied Mathematics, USA, 2009.
[6] J.E. Dennis Jr, R.B. Schnabel, “Numerical Methods for Unconstrained Optimization and Nonlinear Equations”, Society for Industrial and Applied Mathematics, USA, 1996.
[7] J. Nocedal, S.J. Wright, “Numerical optimization”, Springer, USA, 2006.
[8] J.A. Nelder, R. Mead, “A simplex algorithm for function minimization”, Computer Journal, Vol. 7, Issue 4, pp. 308–313, 1965.
[9] J.C. Lagarias, J.A. Reeds, M.H. Wright, P.E. Wright, “Convergence Properties of the Nelder–Mead Simplex Method in Low Dimensions”, SIAM Journal on Optimization, Vol. 9, Issue 1, pp. 112–147, 1998.
[10] J.C. Lagarias, B. Poonen, M.H. Wright, “Convergence of the restricted Nelder–Mead algorithm in two dimensions”, SIAM Journal on Optimization, Vol. 22, Issue 2, pp. 501–532, 2012.
[11] G. Luebeck, R. Meza, “Bhat: General likelihood exploration”, R package version 0.9-10, 2013.
[12] R. Varadhan, “alabama: Constrained Nonlinear Optimization”, R package version 2015.3-1, 2015.