The Generalized Additive Weibull-G Family of Distributions

In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.

[1]  Gauss M. Cordeiro,et al.  A new family of generalized distributions , 2011 .

[2]  Gauss M. Cordeiro,et al.  The Weibull-G Family of Probability Distributions , 2014, Journal of Data Science.

[3]  F. Famoye,et al.  BETA-NORMAL DISTRIBUTION AND ITS APPLICATIONS , 2002 .

[4]  David H. Barlow,et al.  Panic and generalized anxiety disorders: Nature and treatment , 1984 .

[5]  Harshinder Singh,et al.  Reliability Properties of Reversed Residual Lifetime , 2003 .

[6]  D. F. Andrews,et al.  Prognostic Variables for Survival in a Randomized Comparison of Treatments for Prostatic Cancer , 1985 .

[7]  Thiago G. Ramires,et al.  A new generalized Weibull family of distributions: mathematical properties and applications , 2015, Journal of Statistical Distributions and Applications.

[8]  S. Bennett,et al.  Log‐Logistic Regression Models for Survival Data , 1983 .

[9]  Ayman Alzaatreh,et al.  A new method for generating families of continuous distributions , 2013 .

[10]  Morad Alizadeh,et al.  The type I half-logistic family of distributions , 2016 .

[11]  Ramesh C. Gupta.  On Characterization of Distributions by Conditional Expectations , 1975 .

[12]  Kanchan Jain,et al.  Bonferroni Curve and the related statistical inference , 2005 .

[13]  F. Famoye,et al.  Journal of Modern Applied Statistical Methods Gumbel-weibull Distribution: Properties and Applications Recommended Citation Gumbel-weibull Distribution: Properties and Applications , 2022 .

[14]  Gauss M. Cordeiro,et al.  Generalized Beta-Generated Distributions , 2010, Comput. Stat. Data Anal..

[15]  Narayanaswamy Balakrishnan,et al.  On families of beta- and generalized gamma-generated distributions and associated inference , 2009 .

[16]  Maria Longobardi,et al.  Entropy-based measure of uncertainty in past lifetime distributions , 2002, Journal of Applied Probability.

[17]  M. Ward.  The Representation of Stirling's Numbers and Stirling's Polynomials as Sums of Factorials , 1934 .

[18]  Philippe Flajolet,et al.  Singularity Analysis of Generating Functions , 1990, SIAM J. Discret. Math..

[19]  I. Ahmad,et al.  ON THE MEAN INACTIVITY TIME ORDERING WITH RELIABILITY APPLICATIONS , 2004, Probability in the Engineering and Informational Sciences.

[20]  J. Ruiz,et al.  A characterization based on conditional expectations , 1990 .

[21]  Gauss M. Cordeiro,et al.  On the Additive Weibull Distribution , 2014 .

[22]  Dilip Roy,et al.  SOME RESULTS ON REVERSED HAZARD RATE , 2001, Probability in the Engineering and Informational Sciences.

[23]  International Journal of Mathematics And its Applications A New Family of Additive Weibull-Generated Distributions Research , 2016 .

[24]  I. W. Burr.  Cumulative Frequency Functions , 1942 .

[25]  Jorge Navarro,et al.  CHARACTERIZATION THROUGH MOMENTS OF THE RESIDUAL LIFE AND CONDITIONAL SPACINGS , 1998 .

[26]  Harshinder Singh,et al.  The Reversed Hazard Rate Function , 1998, Probability in the Engineering and Informational Sciences.

[27]  M. Kayid,et al.  FURTHER RESULTS INVOLVING THE MIT ORDER AND THE IMIT CLASS , 2005, Probability in the Engineering and Informational Sciences.