An extended-G geometric family

We introduce and study the extended-G geometric family of distributions, which contains as special models some important distributions such as the XTG (Xie et al. 2002) geometric, Weibull geometric, Chen (Chen 2000) geometric, Gompertz geometric, among others. This family not only includes distributions with bathtub and unimodal failure rate functions but provides a broader class of monotone failure rates. Its density function can be expressed as a linear mixture of extended-G densities. We derive explicit expansions for the ordinary and incomplete moments, generating function, mean deviations and Rénvy entropy. The density of the order statistics can also be given as a linear mixture of extended-G densities. The model parameters are estimated by maximum likelihood. The potentiality of the new family is illustrated by means of an application to real data.MSC60E05, 62P10, 62P30

[1]  Gauss M. Cordeiro,et al.  A generalized modified Weibull distribution for lifetime modeling , 2008 .

[2]  G. Cordeiro,et al.  The Weibull-geometric distribution , 2008, 0809.2703.

[3]  Thong Ngee Goh,et al.  A modified Weibull extension with bathtub-shaped failure rate function , 2002, Reliab. Eng. Syst. Saf..

[4]  Samuel Kotz,et al.  The beta exponential distribution , 2006, Reliab. Eng. Syst. Saf..

[5]  Lee J. Bain,et al.  An exponential power life-testing distribution , 1975 .

[6]  Gauss M. Cordeiro,et al.  The Kumaraswamy-Log-Logistic Distribution , 2012 .

[7]  Deo Kumar Srivastava,et al.  The exponentiated Weibull family: a reanalysis of the bus-motor-failure data , 1995 .

[8]  Samuel Kotz,et al.  On some recent modifications of Weibull distribution , 2005, IEEE Transactions on Reliability.

[9]  Peter A. Lachenbruch,et al.  Survival distributions arising from two families and generated by transformations , 1984 .

[10]  Chin-Diew Lai,et al.  A flexible Weibull extension , 2007, Reliab. Eng. Syst. Saf..

[11]  M. Gurvich,et al.  A new statistical distribution for characterizing the random strength of brittle materials , 1997 .

[12]  Hoang Pham,et al.  On Recent Generalizations of the Weibull Distribution , 2007, IEEE Transactions on Reliability.

[13]  D. Kundu,et al.  EXPONENTIATED EXPONENTIAL FAMILY: AN ALTERNATIVE TO GAMMA AND WEIBULL DISTRIBUTIONS , 2001 .

[14]  Gauss M. Cordeiro,et al.  The beta-Weibull geometric distribution , 2013 .

[15]  S. Loukas,et al.  A lifetime distribution with decreasing failure rate , 1998 .

[16]  Gauss M. Cordeiro,et al.  Extended Burr XII Regression Models: Theory and Applications , 2016 .

[17]  Debasis Kundu,et al.  Generalized exponential distribution: different method of estimations , 2001 .

[18]  Hoang Pham.  A Vtub-Shaped Hazard Rate Function with Applications to System Safety , 2002 .

[19]  D. Kundu,et al.  Theory & Methods: Generalized exponential distributions , 1999 .

[20]  Min Xie,et al.  Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function , 1996 .

[21]  Gauss M. Cordeiro,et al.  The beta modified Weibull distribution , 2010, Lifetime data analysis.

[22]  G. S. Mudholkar,et al.  A Generalization of the Weibull Distribution with Application to the Analysis of Survival Data , 1996 .

[23]  Narayanaswamy Balakrishnan,et al.  A General Purpose Approximate Goodness-of-Fit Test , 1995 .

[24]  Saad J. Almalki,et al.  A new modified Weibull distribution , 2013, Reliab. Eng. Syst. Saf..

[25]  Jerald F. Lawless,et al.  Statistical Models and Methods for Lifetime Data: Lawless/Statistical , 2002 .

[26]  John S. White.  The Moments of Log-Weibull Order Statistics , 1969 .

[27]  D. N. Prabhakar Murthy,et al.  A modified Weibull distribution , 2003, IEEE Trans. Reliab..

[28]  M. Nikulin,et al.  A Chi-Squared Test for the Generalized Power Weibull Family for the Head-and-Neck Cancer Censored Data , 2006 .

[29]  J. Lawless.  Statistical Models and Methods for Lifetime Data , 2002 .

[30]  Zhenmin Chen.  A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function , 2000 .

[31]  I. Elbatal,et al.  The modified Weibull geometric distribution , 2015 .

[32]  Gauss M. Cordeiro,et al.  A new distribution with decreasing, increasing and upside-down bathtub failure rate , 2010, Comput. Stat. Data Anal..