On Bivariate Nadarajah-Haghighi Distribution derived from Farlie-Gumbel-Morgenstern copula in the Presence of Covariates

Authors

  • Yakubu Aliyu
    Department of Statistics, Ahmadu Bello University Zaria-Nigeria
  • Umar Usman
    Department of Mathematics, Usmanu Danfodiyo University Sokoto-Nigeria

Keywords:

Exponential Distribution, Nadarajah-Haghighi Distribution, Bivariate Models and Copula Function.

Abstract

An important alternative distribution to the Weibull, generalized exponen-
tial and gamma distributions that is used in survival analysis is the Nadarajah-
Haghighi exponential distribution. Similar to the Weibull, generalized exponen-
tial and gamma distributions, the Nadarajah-Haghighi exponential distribution
is an extension of the well known exponential distribution. In this paper, a copula
function commonly used to model very weak linear dependence was used to intro-
duced a bivariate Nadarajah-Haghighi distribution. The joint survival function,
joint probability density function and joint cumulative distribution were given
in closed form. Bayesian method of estimation was used to estimate the model
parameters considering the presence of right censoring and covariates. Posterior
summaries of interest were obtained via standard Markov Monte Carlo (MCMC )
technique. Two real data sets were used to illustrate the importance and flexi-
bility of the bivariate model in comparison with some competing models. It was
observed that, the bivariate Nadarajah-Haghighi distribution provides a better flt
than bivariate exponential, bivariate Weibull, bivariate generalized exponential
and bivariate modified Weibull distributions.

Dimensions

M. H. Tahir, G. M. Cordeiro, S. Ali, S. Dey & A. Manzoor, “The inverted Nadarajah–Haghighi distribution: estimation methods and applications”, Journal of Statistical Computation and Simulation 88(14) (2018) 2775.

R. D. Gupta & D. Kundu, “Theory & methods: Generalized exponential distributions”, Australian & New Zealand Journal of Statistics 41(2) (1999) 173.

S. Nadarajah & S. Kotz, “The beta exponential distribution”, Reliability engineering & system safety 91(6) (2006) 689.

S. Nadarajah & F. Haghighi, “An extension of the exponential distribution”, Statistics, 45(6) (2011) 543.

A. Yakubu & S. I. Doguwa, “On the properties of the Weibull-Burr III distribution and its application to uncensored and censored survival data”, CBN Journal of Applied Statistics, 8(2) (2017) 91.

J. M. F. Carrasco, E. M. M. Ortega & G. M. Cordeiro, “A generalized modified Weibull distribution for lifetime modeling”, Computational Statistics & Data Analysis 53(2) (2008) 450.

E. M. M. Ortega, G. M. Cordeiro & M. W. Kattan, “The log-beta Weibull regression model with application to predict recurrence of prostate cancer”, Statistical Papers 54(1) (2013) 113.

M. Z. Raqab & D. Kundu, “Burr type X distribution: revisited”, Journal of probability and statistical sciences 4(2) (2006) 179.

A. I. Ishaq, A. Usman, M. Tasi’u, Y. Aliyu & F. A. Idris, “A new WeibullKumaraswamy distribution: Theory and applications”, Nigerian Journal of Scientific Research 16(2) (2017) 158.

I. Shah, B. Iqbal, A. M. Farhan, S. Ali & S. Dey, Unit Nadarajah and

Haghighi distribution: properties and applications in quality control, Scientia Iranica, 2021.

S. Ali, S. Dey, M. H. Tahir & M. Mansoor, “The Poisson NadarajahHaghighi distribution: different methods of estimation”, Journal of Reliability and Statistical Studies (2021) 415

M. Shafqat, S. Ali, I. Shah & S. Dey, “Univariate discrete Nadarajah and Haghighi distribution: Properties and different methods of estimation”, Statistica 80(3) (2020) 301-330

U. Usman, S. Suleiman, B. M. Arkilla & Y. Aliyu, “Nadarajah-Haghighi model for survival data with long term survivors in the presence of right censored data. Pakistan Journal of Statistics and Operation Research 17(3) (2021) 695.

E. M. Almetwally, H. Z. Muhammed & E. S. A. El-Sherpieny, “Bivariate Weibull distribution: properties and different methods of estimation”, Annals of Data Science 7(1) (2020) 163.

X. Bai, Y. Shi, B. Liu, & Q. Fu, “Statistical inference of Marshall-Olkin bivariate Weibull distribution with three shocks based on progressive interval censored data”, Communications in Statistics-Simulation and Computation 48(3) (2019) 637.

E. A. El-Sherpieny, H. Z. Muhammed & E. M. Almetwally, “Fgm bivariate weibull distribution”, In Proceedings of the Annual Conference in Statistics (53rd), Computer Science, and Operations Research, Institute of Statistical Studies and Research, Cairo University (2018) 55.

I. E. Gongsin & F. W. O. Saporu, “A bivariate conditional Weibull distribution with application”, Afrika Matematika 31 (2020) 565.

D. Kundu, & V. Nekoukhou, “On bivariate discrete Weibull distribution’, Communications in Statistics-Theory and Methods 48(14) (2019) 3464.

M. V. D. Peres, J. A. Achcar & E. Z. Martinez, “Bivariate modified Weibull distribution derived from Farlie-Gumbel-Morgenstern copula: a simulation study”, Electronic Journal of Applied Statistical Analysis, 11(2) (2018) 463.

M. El-Morshedy, M. S. Eliwa, A. El-Gohary & A. A. Khalil, “Bivariate exponentiated discrete Weibull distribution: statistical properties, estimation, simulation and applications”, Mathematical Sciences 14(1) (2020) 29.

J. A. Achcar, F. A. Moala, M. H. Tarumoto & L. F. Coladello, “A bivariate generalized exponential distribution derived from copula functions in the presence of censored data and covariates”, Pesquisa Operacional 35 (2015) 165.

R. Alotaibi, M. Khalifa, E. M. Almetwally & I. Ghosh, “Classical and Bayesian Inference of a Mixture of Bivariate Exponentiated Exponential Model”, Journal of Mathematics 2021 (2021) 1.

M. K. A. Elaal & R. S. Jarwan, “Inference of bivariate generalized exponential distribution based on copula functions”, Applied Mathematical Sciences 11(24) (2017) 1155.

D. Kundu & R. D. Gupta, “Absolute continuous bivariate generalized exponential distribution”, AStA Advances in Statistical Analysis 95(2) (2011) 169.

S. M. Mirhosseini, M. Amini, D. Kundu & A. Dolati, “On a new absolutely continuous bivariate generalized exponential distribution”, Statistical Methods and Applications 23 (2014)

S. M. Mirhosseini, M. Amini, D. Kundu & A. Dolati, “On a new absolutely continuous bivariate generalized exponential distribution”, Statistical Methods & Applications 24(1) (2015) 61.

E. S. A. El-Sherpieny, E. M. Almetwally & H. Z. Muhammed, “Bayesian and non-bayesian estimation for the parameter of bivariate generalized Rayleigh distribution based on clayton copula under progressive type-II censoring with random removal”, Sankhya A 2021 (2021) 1.

H. Z. Muhammed, “Bivariate inverse Weibull distribution”, Journal of Statistical Computation and Simulation 86(12) (2016) 2335.

D. Kundu & A. K. Gupta, “On bivariate inverse Weibull distribution”, Brazilian Journal of Probability and Statistics 31(2) (2017) 275.

A. S. Al-Moisheer, R. M. Alotaibi, G. A. Alomani & H. Rezk, “Bivariate mixture of inverse Weibull distribution: properties and estimation”, Mathematical Problems in Engineering 2020 (2020) 1.

M. S. Eliwa & M. El-Morshedy, “Bayesian and non-Bayesian estimation of four-parameter of bivariate discrete inverse Weibull distribution with applications to model failure times, football and biological data”, Filomat 34(8) (2020) 2511.

H. Z. Muhammed, & E. M. Almetwally, “Bayesian and non-Bayesian estimation for the bivariate inverse weibull distribution under progressive type-II censoring”, Annals of Data Science 10 (2023) 481.

S. Mondal & D. Kundu, “A bivariate inverse Weibull distribution and its application in complementary risks model”, Journal of Applied Statistics 47(6) (2020) 1084

E. M. Almetwally & H. Z. Muhammed, “On a bivariate FrA˜ c chet distribution”, J Stat Appl Probab 9(1) (2020) 1.

H. Z. Muhammed, E. S. A. El-Sherpieny & E. M. Almetwally, ”Dependency measures for new bivariate models based on copula function”, Information Sciences Letters 10(3) (2021) 15.

S. Ali, M. Shafqat, I. Shah & S. Dey, “Bivariate discrete Nadarajah and Haghighi distribution: properties and different methods of estimation”, Filomat 33(17) (2019) 5589.

U. Usman & Y. Aliyu, “Bivariate Nadarajah-Haghighi distribution derived from copula functions: Bayesian estimation and applications”, Benin Journal of Statistics 5 (2022) 45.

D. Morgenstern, “Einfache beispiele zweidimensionaler verteilungen”, Mitteilingsblatt fur Mathematische Statistik, 8 (1956) 234.

D. J. G. Farlie, “The performance of some correlation coefficients for a general bivariate distribution”, Biometrika 47(3/4) (1960) 307.

E. J. Gumbel, “Bivariate exponential distributions”, Journal of the American Statistical Association 55(292) (1960) 698.

P. K. Trivedi & D. M. Zimmer, ”Copula modeling: an introduction for practitioners”, Foundations and Trends R in Econometrics 1(1) (2007) 1.

E. Z. Martinez, J. A. Achcar & T. R. Icuma, “Bivariate Basu-Dhar geometric model for survival data with a cure fraction”, Electronic Journal of Applied Statistical Analysis 11(2) (2018) 655.

D. J. Spiegelhalter, N. G. Best, B. P. Carlin & A. Van Der Linde, “Bayesian measures of model complexity and fit”, Journal of the royal statistical society: Series b (statistical methodology) 64(4) (2002) 583.

C. A. McGilchrist & C. W. Aisbett, ”Regression with frailty in survival analysis”, Biometrics, (1991) 461.

G. John, C. Louis, A. Berner & D. Genne, “Tobacco stained fingers and´ its association with death and hospital admission: A retrospective cohort study”, PloS one 10(9) (2015) e0138211.

Published

2023-05-01

How to Cite

On Bivariate Nadarajah-Haghighi Distribution derived from Farlie-Gumbel-Morgenstern copula in the Presence of Covariates. (2023). Journal of the Nigerian Society of Physical Sciences, 5(2), 871. https://doi.org/10.46481/jnsps.2023.871

Issue

Volume 5, Issue 2, May 2023

Section

Original Research
Copyright & Licensing

Copyright (c) 2023 Yakubu Aliyu, Umar Usman

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

On Bivariate Nadarajah-Haghighi Distribution derived from Farlie-Gumbel-Morgenstern copula in the Presence of Covariates. (2023). Journal of the Nigerian Society of Physical Sciences, 5(2), 871. https://doi.org/10.46481/jnsps.2023.871

Similar Articles

71-80 of 191

You may also start an advanced similarity search for this article.