Properties and methods of estimation for a bivariate exponentiated Fréchet distribution
-
Abdus Saboor
,
Hassan S. Bakouch
Abstract
In this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed bivariate distribution with other related bivariate distributions are fitted to a real-life paired data set. It is shown that, the BvEF distribution has a superior performance among the compared distributions using several tests of goodness–of–fit.
(Communicated by Gejza Wimmer)
References
[1] Arnold, B.: A note on multivariate distributions with spedified marginal, J. Amer. Statist. Assoc. 62 (1967), 1460–1461.10.1080/01621459.1967.10500946Suche in Google Scholar
[2] Akaike, H.: A new look at the statistical model identification, IEEE Trans. Automat. Control 19 (1974), 716–723.10.1007/978-1-4612-1694-0_16Suche in Google Scholar
[3] Babu, M. G.—Jayakumar, K.: A new bivariate distribution with modified Weibull distribution as marginals, J. Indian Soc. Probab. Stat. 19 (2018), 271–297.10.1007/s41096-018-0043-2Suche in Google Scholar
[4] Dobrowolski, E.—Kumar, P.: Some properties of the Marshall-Olking and generalized Cuadras-Augé families of copulas, Aust. J. Math. Anal. Appl. 11(1) (2014), 1–13.Suche in Google Scholar
[5] Efron, B.: The Jackknife, the Bootstrap, and Other Resampling Plans. In: CBMS-NSF Regional Conference Series in Appl. Math., Monograph 38, 1982.10.1137/1.9781611970319Suche in Google Scholar
[6] El-Gohary, A.—El-Bassiouny, A. H.—El-Morshedy, M.: Bivariate exponentiated modified Weibull extension distribution, J. Stat. Appl. Prob. 5(1) (2016), 67–78.10.18576/jsap/050106Suche in Google Scholar
[7] Embrecht, P.—Lindskog, F.—Mcneil, A.: Modelling Dependence with Copulas and Applications to Risk Management. In: Handbook of Heavy Tailed Distributions in Finance (S. Rachev ed.), Elsevier, 2003.10.1016/B978-044450896-6.50010-8Suche in Google Scholar
[8] Fréchet, M.: Sur la loi de probabilite delecart maximum, Anna. de la soci. Polo. de Math. 6 (1927), 93–116Suche in Google Scholar
[9] Kundu, R. D.—Gupta, R. D.: Bivariate generalized exponential distribution, J. Multivariate Anal. 100(4) (2009), 581–593.10.1016/j.jmva.2008.06.012Suche in Google Scholar
[10] Al-Khedhairi—El-Gohary, A.: A new class of bivariate Gompertz distributions and its mixture, Int. J. Math. Anal. 2(5) (2008), 235–253.Suche in Google Scholar
[11] Marshall, W.—Olkin, A.: A multivariate exponential distribution, J. Amer. Statist. Assoc. 62 (1967), 30–44.10.21236/AD0634335Suche in Google Scholar
[12] Kotz, S.—Nadarajah, S.: Extreme Value Distributions, Theory and Applications, Imperial College Press, London, 2000.10.1142/p191Suche in Google Scholar
[13] Muhammed, H. Z.: Bivariate inverse Weibull distribution, J. Stat. Comput. Simul. 86 (2016), 2335–2345.10.1080/00949655.2015.1110585Suche in Google Scholar
[14] Nelsen, R. B.: An Introduction to Copulas, Springer, New York, 2006.Suche in Google Scholar
[15] Sarhan, A.—Balakrishnan, N.: A new class of bivariate distributions and its mixture, J. Multivariate Anal. 98 (2007), 1508–1527.10.1016/j.jmva.2006.07.007Suche in Google Scholar
[16] Sklar, A.: Functions de repartition à n-dimensions et leurs marges, Inst. Stat. University Paris 8 (1959), 229–231.Suche in Google Scholar
[17] Welsh, A. H.—Csorgo, S.: Testing for exponential and Marshall-Olkin distribution, J. Stat. Plan. Infe. 23 (1989), 287–300.10.1016/0378-3758(89)90073-6Suche in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- Monadic pseudo BE-algebras
- Quadruple construction of decomposable double MS-algebras
- Fibonacci numbers in generalized Pell sequences
- Solutions of a generalized markoff equation in Fibonacci numbers
- Root separation for polynomials with reducible derivative
- Quadratic refinements of Young type inequalities
- Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means
- Integration with respect to deficient topological measures on locally compact spaces
- Differential subordinations and Pythagorean means
- Analogs of Hayman’s Theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded L-index in joint variables
- Unbounded oscillation of fourth order functional differential equations
- Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term
- Entropy as an integral operator: Erratum and modification
- Unital topology on a unital l-group
- On the topological complexity of Grassmann manifolds
- Properties and methods of estimation for a bivariate exponentiated Fréchet distribution
- Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses
- Two semigroup rings associated to a finite set of meromorphic functions
Artikel in diesem Heft
- Regular papers
- Monadic pseudo BE-algebras
- Quadruple construction of decomposable double MS-algebras
- Fibonacci numbers in generalized Pell sequences
- Solutions of a generalized markoff equation in Fibonacci numbers
- Root separation for polynomials with reducible derivative
- Quadratic refinements of Young type inequalities
- Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means
- Integration with respect to deficient topological measures on locally compact spaces
- Differential subordinations and Pythagorean means
- Analogs of Hayman’s Theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded L-index in joint variables
- Unbounded oscillation of fourth order functional differential equations
- Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term
- Entropy as an integral operator: Erratum and modification
- Unital topology on a unital l-group
- On the topological complexity of Grassmann manifolds
- Properties and methods of estimation for a bivariate exponentiated Fréchet distribution
- Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses
- Two semigroup rings associated to a finite set of meromorphic functions
