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#### Cícero R. B. Dias [1] , Morad Alizadeh [2] , Gauss M. Cordeiro [3]

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Recently, there has been a great interest among statisticians and applied researchers in constructing flexible distributions for better modeling
non-monotone failure rates. We study a lifetime model of the beta generated family, called the beta Nadarajah-Haghighi distribution, which can be used to model survival data. The proposed model includes as special models some important distributions. The hazard rate function is an important quantity characterizing life phenomena. Its hazard function can be constant, decreasing, increasing, upsidedown bathtub and bathtub-shaped depending on the parameters. We provide a comprehensive mathematical treatment of the new distribution and derive explicit expressions for some of its basic mathematical quantities. The method of maximum likelihood is used for estimating the model parameters and a small Monte Carlo simulation is conducted. We fit the proposed model to two real data sets to prove empirically its flexibility as compared to other lifetime distributions
Beta distribution, Moment, Nadarajah-Haghighi distribution, Mean deviation
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Primary Language en Mathematics Statistics Author: Cícero R. B. Dias (Primary Author)Institution: DEPARTAMENTO DE ESTATÍSTICA, UNIVERSIDADE FEDERAL DE PERNAMBUCO, BRAZILCountry: Brazil Author: Morad AlizadehInstitution: DEPARTMENT OF STATISTICS, FACULTY OF SCIENCES, PERSIAN GULF UNIVERSITYCountry: Iran Author: Gauss M. CordeiroInstitution: DEPARTAMENTO DE ESTATÍSTICA, UNIVERSIDADE FEDERAL DE PERNAMBUCOCountry: Brazil
 Bibtex @research article { hujms471211, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe University}, year = {2018}, volume = {47}, pages = {1302 - 1320}, doi = {}, title = {The beta Nadarajah-Haghighi distribution}, key = {cite}, author = {Dias, Cícero R. B. and Alizadeh, Morad and Cordeiro, Gauss M.} } APA Dias, C , Alizadeh, M , Cordeiro, G . (2018). The beta Nadarajah-Haghighi distribution. Hacettepe Journal of Mathematics and Statistics, 47 (5), 1302-1320. Retrieved from http://dergipark.gov.tr/hujms/issue/39860/471211 MLA Dias, C , Alizadeh, M , Cordeiro, G . "The beta Nadarajah-Haghighi distribution". Hacettepe Journal of Mathematics and Statistics 47 (2018): 1302-1320 Chicago Dias, C , Alizadeh, M , Cordeiro, G . "The beta Nadarajah-Haghighi distribution". Hacettepe Journal of Mathematics and Statistics 47 (2018): 1302-1320 RIS TY - JOUR T1 - The beta Nadarajah-Haghighi distribution AU - Cícero R. B. Dias , Morad Alizadeh , Gauss M. Cordeiro Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1302 EP - 1320 VL - 47 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2016 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics The beta Nadarajah-Haghighi distribution %A Cícero R. B. Dias , Morad Alizadeh , Gauss M. Cordeiro %T The beta Nadarajah-Haghighi distribution %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 5 %R %U ISNAD Dias, Cícero R. B. , Alizadeh, Morad , Cordeiro, Gauss M. . "The beta Nadarajah-Haghighi distribution". Hacettepe Journal of Mathematics and Statistics 47 / 5 (October 2018): 1302-1320.