Generalised Odd Frechet Family of Distributions: Properties and Applications

Shahdie Marganpoor; Vahid Ranjbar; Morad  Alizadeh; Kamel  Abdollahnezhad

doi:DOI 10.21307/stattrans-2020-047

Generalised Odd Frechet Family of Distributions: Properties and Applications

Shahdie Marganpoor Golestan University, Gorgan, 49138-15739, Iran , Vahid Ranjbar Golestan University, Gorgan, 49138-15739, Iran ORCID:https://orcid.org/0000-0003-3743-0330 , Morad Alizadeh Persian Gulf University, Bushehr, 751691-3798, Iran ORCID:https://orcid.org/0000-0001-6638-2185 , Kamel Abdollahnezhad Golestan University, Gorgan, 49138-15739, Iran Statistics in Transition new series, vol. 21, 2020, 3, pages: 109-128 Published online: 4 September 2020 DOI DOI 10.21307/stattrans-2020-047

750 Views 29 Downloads

ARTICLE

(English) PDF

ABSTRACT

A new distribution called Generalized Odd Fréchet (GOF) distribution is presented and its properties explored. Some structural properties of the proposed distribution, including the shapes of the hazard rate function, moments, conditional moments, moment generating function, skewness, and kurtosis are presented. Mean deviations, Lorenz and Bonferroni curves, Rényi entropy, and the distribution of order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters, and finally applications of the model to a real data set are presented to illustrate the usefulness of the proposed distribution.

KEYWORDS

Fréchet distribution, Wiebull distribution, structural properties, failure-time, maximum likelihood estimation.

REFERENCES

AFIFY A.Z., ALIZADEH, M., YOUSOF, H. M., ARYAL, G. and AHMAD, M. (2016a). The transmuted geometric-G family of distributions: theory and applications. Pak. J. Statist., 32(), pp. 139–160.

AFIFY A.Z., CORDEIRO, G. M., YOUSOF, H. M., ALZAATREH, A. and NOFAL, Z. M. (2016b). The Kumaraswamy transmuted-G family of distributions: properties and applications. J. Data Sci., 14(2), pp. 245–270.

AFIFY, A.Z., YOUSOF, H.M. and NADARAJAH, S. (2016c). The beta transmuted-H family of distributions: properties and applications. Statistics and its Inference, 10(3), pp. 505–520.

ALEXANDER, C., CORDEIRO, G.M., ORTEGA, E.M.M. and SARABIA, J.M. (2012). Generalized beta generated distributions, Computational Statistics and Data Analysis, 56, pp. 1880–1897.

ALIZADEH, M., CORDEIRO, G. M., DE BRITO, E. and DEMÉTRIO C.G.B. (2015a). The beta Marshall- Olkin family of distributions. Journal of Statistical Distributions and Applications, 23(3), pp. 546–557.

ALIZADEH, M., CORDEIRO, G.M., MANSOOR, M., ZUBAIR, M. and HAMEDANI, G.G. (2015b). The Kumaraswamy Marshal-Olkin family of distributions. Journal of the Egyptian Mathematical Society, 23, pp. 546–557.

ALIZADEH, M., MEROVCI, F. and HAMEDANI, G.G. (2015c). Generalized transmuted family of distributions: properties and applications. Hacettepa Journal of Mathematics and Statistics, 46(4), pp. 645–667.

ALIZADEH M., EMADI M., DOOSTPARAST M., CORDEIRO G.M., ORTEGA E.M.M. and PESCIM R.R., (2016) A new family of distributions: the Kumaraswamy odd loglogistic, properties and applications. Hacettepe Journal of Mathematics and Statistics, 44(6), pp. 1491–1512.

ALIZADEH, M., CORDEIRO, G.M., NASCIMENTO, A.D.C. LIMA M.D.S. AND ORTEGA, E.M.M. (2016a). Odd-Burr generalized family of distributions with some applications. Journal of Statistical Computation and Simulation, 83, pp. 326–339.

ALIZADEH, M., YOUSOF, H.M., AFIFY A.Z., CORDEIRO, G.M., and MANSOOR, M. (2016b). The complementary generalized transmuted Poisson-G family. Austrian Journal of Statistics, 47(4), pp. 60–80.

ALIZADEH, M., ALTUN, E., CORDEIRO, G. M., and RASEKHI, M. (2018). The odd power cauchy family of distributions: properties, regression models and applications.Journal of Statistical Computation and Simulation, 88(4), pp. 785–807.

ALZAATREH, A., LEE, C. and FAMOYE, F. (2013). A new method for generating families of con- tinuous distributions. Metron, 71, pp. 63–79.

ALZAGHAL, A., FAMOYE, F. and LEE, C. (2013). Exponentiated T-X family of distributions with some applications. International Journal of Probability and Statistics, 2, pp. 31–49.

ANDRADE NLR, MOURA RMP, SILVEIRA A (2007) Determinaçao da Q7,10 para o Rio Cuiab ´ a, Mato Grosso, Brasil e comparaçao com a vazao regularizada após a implantaçao do reservatório de aproveitamento múltiplo de manso. 24o Congresso Brasileiro de Engenharia Sanitária e Ambiental. Belo Horizonte, Minas Gerais Brasil.

BOURGUIGNON, M., SILVA, R.B. and CORDEIRO, G.M. (2014). The WeibullG family of probability distributions, Journal of Data Science, 12, pp. 53–68.

CORDEIRO, G. M., DE CASTRO, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81, pp. 883–898.

CORDEIRO, GAUSS M., SARALEES NADARAJAH, and EDWINMMORTEGA, (2012). The Kumaraswamy Gumbel distribution. Statistical Methods and Applications, 21.2, pp. 139–168.

CORDEIRO, G. M., GOMES, A. E., DA-SILVA, C. Q. and ORTEGA, E. M., (2013). The beta exponentiated Weibull distribution. Journal of Statistical Computation and Simulation, 83, pp. 114–138.

CORDEIRO, G. M., HASHIMOTO, E. M. and ORTEGA, E. M., (2014). McDonald Weibull model. Statistics: A Journal of Theoretical and Applied Statistics, 48, pp. 256–278.

CORDEIRO, G. M.,ALIZADEH, M., TAHIR, M. H., MANSOOR, M., BOURGUIGNON, M., & HAMEDANI, G. G., (2015). The beta odd log-logistic generalized family of distributions, Hacettepe Journal of Mathematics and Statistics, 45(73), pp. 126–139.

CORDEIRO, G. M., ALIZADEH, M. and DINIZ MARINHO, P. R., (2016a). The type I half-logistic family of distributions. Journal of Statistical Computation and Simulation, 86, pp. 707–728.

CORDEIRO, G. M., ALIZADEH, M., ORTEGA, E. M. and SERRANO, L. H., V.(2016b). The Zografos- Balakrishnan odd log-logistic family of distributions: Properties and Applications. Hacet. J. Math. Stat., 7(1), pp. 211–234.

CORDEIRO, G. M., ALIZADEH, M., OZEL, G., HOSSEINI, B., ORTEGA, E. M. M. and ALTUN, E., (2016c). The generalized odd log-logistic family of distributions: properties, regression models and applications, Journal of Statistical Computation and Simulation, 87, pp. 908–932.

CORDEIRO, G. M., ALIZADEH, M., TAHIR, M. H., MANSOOR, M., BOURGUIGNON, M. and HAMEDANI G. G., (2016d). The beta odd log-logistic generalized family of distributions, Hacettepe Journal of Mathematics and Statistics, 45(6), pp. 1175–1202.

CORDEIRO, G. M., ALIZADEH, M., OZEL, G., HOSSEINI, B., ORTEGA, E. M. M. and ALTUN, E., (2017). The generalized odd log-logistic family of distributions: properties, regression models and applications. Journal of Statistical Computation and Simulation, 87(5), pp. 908–932.

EMLET, R. B., MCEDWARD, L. R. and STRATHMANN, R. R., (1987) Echinoderm larval ecology viewed from the egg, in: M. Jangoux and J.M. Lawrence (Eds.) Echinoderm Studies,2, pp. 55–136.

EUGENE, N., LEE, C. and FAMOYE, F., (2002). Beta-normal distribution and its applications. Commun. Stat. Theory Methods, 31, pp. 497–512.

GRADSHTEYN, I. S., RYZHIK, I. M., (2000). Table of integrals, series, and products. Academic Press, San Diego.

GUPTA, R. C., GUPTA, P. L. and GUPTA, R. D., (1998). Modeling failure time data by Lehmann alternatives. Commun. Stat. Theory Methods, 27, pp. 887–904.

HAGHBIN H., OZEL G., ALIZADEH, M. and HAMEDANI, G. G., (2017) A new generalized odd log-logistic family of distributions. Communications in Statistics – Theory and Methods, 46(20), pp. 9897–9920.

KORKMAZ, M. C., GENC, A. I., (2016). A new generalized two-sided class of distributions with an emphasis on two-sided generalized normal distribution. Communications in Statistics - Simulation and Computation, 46, pp. 1441–1460.

KORKMAZ, M. C., (2018). A new family of the continuous distributions: the extended Weibull-G family. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), pp. 248–270.

KORKMAZ, M. C. , YOUSOF H. M., HAMEDANI, G. G. and ALI, M. M., (2018). The Marshall-Olkin Generalized G Poisson Family of Distributions, Pakistan Journal of Statistics, 34(3), pp. 251–267.

LEHMANN, E. L., CASELLA, G., (1998) Theory of Point Estimation, Springer.

MARSHALL, A.W., OLKIN, I., (1997). A new methods for adding a parameter to a family of distributions with application to the Exponential andWeibull families. Biometrika, 84, pp. 641–652.

MEROVCI, F., ALIZADEH, M. and HAMEDANI, G. G., (2016). Another generalized transmuted family of distributions: properties and applications, Austrian Journal of Statistics, 45, pp. 71–93.

MEROVCI, F., ALIZADEH, M., YOUSOF, H. M. and HAMEDANI, G. G., (2016). The exponentiated transmuted-G family of distributions: theory and applications. Commun. Stat. Theory Meth- ods, 46(21), pp. 10800–10822.

NOFAL, Z. M., AFIFY, A. Z., YOUSOF, H. M. and CORDEIRO, G. M., (2017). The generalized transmuted-G family of distributions. Commun. Stat. Theory Methods,46(8), pp. 4119–4136.

SILVA, F. G., PERCONTINI, A., DE BRITO, E., RAMOS, M. W., VENANCIO, R. and CORDEIRO, G. M., (2016). The odd Lindley-G family of distributions, Austrian Journal of Statistics, VV, 1–xx.

TAHIR, M. H., CORDEIRO, G. M., ALZAATREH, A., MANSOOR, M. and ZUBAIR, M., (2016a). The logistic- X family of distributions and its applications. Commun. Stat. Theory Methods,45(24), pp. 7326–7349.

TAHIR, M. H., ZUBAIR, M., MANSOOR, M., CORDEIRO, G. M., ALIZADEH, M. and HAMEDANI, G. G., (2016b). A new Weibull-G family of distributions. Hacet. J. Math. Stat.,45 (2), pp. 629–647.

YOUSOF, H. M., AFIFY, A. Z., ALIZADEH, M., BUTT, N. S., HAMEDANI, G. G. and ALI, M. M., (2015). The transmuted exponentiated generalized-G family of distributions, Pak. J. Stat. Oper. Res., 11, pp. 441–464.

YOUSOF, H. M., AFIFY, A. Z., HAMEDANI, G. G. and ARYAL, G., (2016). the Burr X generator of distributions for lifetime data. Journal of Statistical Theory and Applications, 16(3), pp. 288–305.

YOUSOF, H. M., ALTUN, E., RAMIRES, T. G., ALIZADEH, M., and RASEKHI, M., (2018). A new family of distributions with properties, regression models and applications. Journal of Statistics and Management Systems, 21(1), pp. 163–188.

ZOGRAFOS, K., BALAKRISHNAN, N., (2009). On families of beta and generalized gamma-generated distributions and associated inference. Statistical Methodology, 6, pp. 344–362.