The Fréchet Topp Leone-G Family of Distributions: Properties, Characterizations and Applications
Tóm tắt
A new family of continuous distributions which ensure model flexiblity, is introduced based on the Fréchet distribution and Topp Leone-G family. Two special sub-models of the new family are discussed. We provide some distributional properties of this family in the general setting such as the series expansions of density, moments, generating function, stress strength model, Rényi and Shannon entropies, probability weighted moments and order statistics. Certain characterizations of the proposed family are presented. The maximum likelihood estimates and the observed information matrix are obtained for the model parameters. We assess the performance of the maximum likelihood estimators by means of a graphical simulation study. The potentiality of the new class is shown via two applications to real data sets.
Tài liệu tham khảo
Afify AZ, Altun E, Alizadeh M, Ozel G, Hamedani GG (2017) The odd exponentiated half-logistic-G family: properties, characterizations and applications. Chil J Stat 8:65–91
Afify AZ, Nofal ZM, Yousof HM, El Gebaly YM, Butt NS (2015) The transmuted Weibull Lomax distribution: properties and application. Pak J Stat Oper Res 11:135–152
Afify AZ, Yousof HM, Nadarajah S (2017) The beta transmuted-H family of distributions: properties and applications. Stat Interference 10:505–520
Alizadeh M, Altun E, Afify AZ, Ozel G (2018) The extended odd Weibull-G family: properties and applications. Commun Fac Sci Univ Ank Ser A1 Math Stat 68:161–186
Alizadeh M, Cordeiro GM, Nascimento ADC, Lima MDS, Ortega EMM (2016) Odd-Burr generalized family of distributions with some applications. J Stat Comput Simul 83:326–339
Alizadeh M, Tahmasebi S, Haghbin H (2018) The exponentiated odd log-logistic family of distributions: properties and applications. J Stat Model Theory Appl 1:1–24
Alizadeh M, Yousof HM, Afify AZ, Cordeiro GM, Mansoor M (2018) The complementary generalized transmuted Poisson-G family of distributions. Austrian J Stat 47:54–71
Al-Shomrani A, Arif O, Shawky K, Hanif S, Shahbaz MQ (2016) Topp-Leone family of distributions: some properties and application. Pak J Stat Oper Res 12:443–451
Alzaatreh A, Lee C, Famoye F (2013) A new method for generating families of continuous distributions. Metron 71:63–79
Brito E, Cordeiro GM, Yousof HM, Alizadeh M, Silva GO (2017) Topp-Leone odd log-logistic family of distributions. J Stat Comput Simul 87:3040–3058
Cordeiro GM, Ortega EMM, Popović BV, Pescim RR (2014) The Lomax generator of distributions: properties, minification process and regression model. Appl Math Comput 247:465–486
Glanzel W (1987) A characterization theorem based on truncated moments and its application to some distribution families. In: Mathematical statistics and probability theory (Bad Tatzmannsdorf, 1986), vol 7. Reidel, Dordrecht, pp 75–84
Glanzel W (1990) Some consequences of a characterization theorem based on truncated moments. Stat J Theor Appl Stat 21:613–618
Hamedani GG (2013) On certain generalized gamma convolution distributions II, Technical Report. 484, 2013, MSCS, Marquette University
Hamedani GG, Yousof HM, Rasekhi M, Alizadeh M, Najibi SM (2018) Type I general exponential class of distributions. Pak J Stat Oper Res 14:39–55
Korkmaz MÇ, Alizadeh M, Yousof HM, Butt NS (2018) The generalized odd Weibull generated family of distributions: statistical properties and applications. Pak J Stat Oper Res 14:541–556
Korkmaz MÇ, Altun E, Yousof HM, Hamedani GG (2019) The odd power Lindley generator of probability distributions: properties, characterizations and regression modeling. Int J Stat Probab 8:70–89
Lee ET, Wang JW (2003) Statistical methods for survival data analysis, 3rd edn. Wiley, New York
Lemonte A, Cordeiro GM (2013) An extended Lomax distribution. Statistics 47:800–816
Mansour MM, Abd Elrazik EM, Afify AZ, Ahsanullah M, Altun E (2019) The transmuted transmuted-G family: properties and applications. J Nonlinear Sci Appl 12:217–229
Mead ME (2016) On five-parameter Lomax distribution: properties and applications. Pak J Stat Oper Res 12:185–199
Nassar M, Kumar D, Dey S, Cordeiro GM, Afify AZ (2019) The Marshall-Olkin alpha power family of distributions with applications. J Comput Appl Math 351:41–53
Proschan F (1963) Theoretical explanation of observed decreasing failure rate. Technometrics 5:375–383
Reyad H, Jamal F, Othman S, Hamedani GG (2018) The transmuted Gompertz-G family of distributions: properties and applications. Tbilisi Math J 11:47–67
Reyad H, Jamal F, Othman S, Hamedani GG (2018) The transmuted odd Lindley-G family of distributions. Asian J Probab Stat 1:1–25
Reyad H, Alizadeh M, Jamal F, Othman S (2018) The Topp Leone odd Lindley-G family of distributions: properties and applications. J Stat Manag Syst 21:1273–1297
Tahir MH, Cordeiro GM, Mansoor M, Zubair M (2015) The Weibull-Lomax distribution: properties and applications. Hacettepe J Math Stati 44:461–480
Yousof HM, Afify AZ, Hamedani GG, Aryal G (2017) The Burr X generator of distributions for lifetime data. J Stat Theory Appl 16:288–305
Yousof HM, Rasekhi M, Altun E, Alizadeh M (2019) The extended odd Fréchet family of distributions: properties, applications and regression modeling. Int J Math Comput 30:1–16