The exponentiated generalized Birnbaum-Saunders distribution

A new distribution called the exponentiated generalized Birnbaum-Saunders distribution is proposed and studied. The new distribution is quite flexible to model survival data, reliability problems, fatigue life studies and hydrological data. It can have decreasing, increasing, upside-down bathtub, bathtub-shaped, increasing-decreasing-increasing and decreasing-increasing-decreasing hazard rate functions. We provide a comprehensive account of the mathematical properties of the new distribution and various structural quantities are derived. We discuss maximum likelihood estimation of the model parameters for uncensored and censored data. Two empirical applications of the new model to real data are presented for illustrative purposes.

[1]  Debasis Kundu,et al.  Modified moment estimation for the two-parameter Birnbaum-Saunders distribution , 2003, Comput. Stat. Data Anal..

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

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

[4]  E. K. Al-Hussaini,et al.  Inference based on censored samples from exponentiated populations , 2010 .

[5]  Francisco Cribari-Neto,et al.  Improved statistical inference for the two-parameter Birnbaum-Saunders distribution , 2007, Comput. Stat. Data Anal..

[6]  Gilberto A. Paula,et al.  Generalized Birnbaum‐Saunders distributions applied to air pollutant concentration , 2008 .

[7]  Pushpa L. Gupta,et al.  Modeling failure time data by lehman alternatives , 1998 .

[8]  J. Moors,et al.  A quantile alternative for kurtosis , 1988 .

[9]  Gauss M. Cordeiro,et al.  The beta-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling , 2011, Comput. Stat. Data Anal..

[10]  Bing Xing Wang,et al.  Generalized interval estimation for the Birnbaum-Saunders distribution , 2012, Comput. Stat. Data Anal..

[11]  S. Nadarajah,et al.  The exponentiated Weibull distribution: a survey , 2013 .

[12]  James B. McDonald,et al.  Some Generalized Functions for the Size Distribution of Income , 1984 .

[13]  A. Desmond.  Stochastic models of failure in random environments , 1985 .

[14]  Narayanaswamy Balakrishnan,et al.  Acceptance Sampling Plans from Truncated Life Tests Based on the Generalized Birnbaum–Saunders Distribution , 2007, Commun. Stat. Simul. Comput..

[15]  Vartan Choulakian,et al.  Goodness-of-Fit Tests for the Generalized Pareto Distribution , 2001, Technometrics.

[16]  Magne Vollan Aarset,et al.  How to Identify a Bathtub Hazard Rate , 1987, IEEE Transactions on Reliability.

[17]  G. S. Mudholkar,et al.  Exponentiated Weibull family for analyzing bathtub failure-rate data , 1993 .

[18]  Ramesh C. Gupta,et al.  Analyzing skewed data by power normal model , 2008 .

[19]  Gauss M. Cordeiro,et al.  Computational Statistics and Data Analysis a Generalized Modified Weibull Distribution for Lifetime Modeling , 2022 .

[20]  Narayanaswamy Balakrishnan,et al.  Estimation in the Birnbaum-Saunders distribution based on scale-mixture of normals and the EM-algorithm , 2009 .

[21]  Z. Birnbaum,et al.  A new family of life distributions , 1969 .

[22]  Artur J. Lemonte,et al.  Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples , 2010, Comput. Stat. Data Anal..

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

[24]  R. Terras.  A miller algorithm for an incomplete bessel function , 1981 .

[25]  P. Kumaraswamy.  A generalized probability density function for double-bounded random processes , 1980 .

[26]  Gauss M. Cordeiro,et al.  The exponentiated Kumaraswamy distribution and its log-transform , 2013 .

[27]  Simos G. Meintanis.  Inference procedures for the Birnbaum-Saunders distribution and its generalizations , 2010, Comput. Stat. Data Anal..

[28]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[29]  Ingram Olkin,et al.  Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families , 2007 .

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

[31]  Francisco Cribari-Neto,et al.  Bootstrap-based improved estimators for the two-parameter Birnbaum–Saunders distribution , 2008 .

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

[33]  Debasis Kundu,et al.  On the hazard function of Birnbaum-Saunders distribution and associated inference , 2008, Comput. Stat. Data Anal..

[34]  Y. H. Abdelkader,et al.  Computing the moments of order statistics from nonidentical random variables , 2004 .

[35]  Samuel Kotz,et al.  The Exponentiated Type Distributions , 2006 .

[36]  Ayman Alzaatreh,et al.  Methods for generating families of univariate continuous distributions in the recent decades , 2013 .

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

[38]  Debasis Kundu,et al.  Inference and optimal censoring schemes for progressively censored Birnbaum–Saunders distribution , 2013 .

[39]  Sam C. Saunders,et al.  Reliability, Life Testing and the Prediction of Service Lives: For Engineers and Scientists (Springer Series in Statistics) , 2010 .

[40]  Yincai Tang,et al.  Computational Statistics and Data Analysis Reference Analysis for Birnbaum–saunders Distribution , 2022 .

[41]  Víctor Leiva,et al.  A Non-Central Version of the Birnbaum-Saunders Distribution for Reliability Analysis , 2009, IEEE Transactions on Reliability.

[42]  Chad R. Bhatti,et al.  The Birnbaum-Saunders autoregressive conditional duration model , 2010, Math. Comput. Simul..

[43]  Gauss M. Cordeiro,et al.  The exponentiated generalized inverse Gaussian distribution , 2011 .

[44]  Saralees Nadarajah,et al.  The exponentiated exponential distribution: a survey , 2011 .

[45]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[46]  José M. Angulo,et al.  A length-biased version of the Birnbaum-Saunders distribution with application in water quality , 2009 .

[47]  Gauss M. Cordeiro,et al.  The Exponentiated Generalized Class of Distributions , 2021, Journal of Data Science.