Journal of Statistical Computation and Simulation Vol. 78, No. 11, November 2008, 1105–1118 Random number generators for the generalized Birnbaum–Saunders distribution VÍCTOR LEIVA*†,ANTONIO SANHUEZA‡, PRANAB K. SEN§ and GILBERTO A. PAULA¶ †Departamento de Estadística, Universidad de Valparaíso, Casilla de correos 5030, Valparaíso, Chile ‡Departamento de Matemática y Estadística, Universidad de La Frontera, Temuco, Chile §Department of Biostatistics, University of North Carolina, Chapel Hill, USA ¶Departamento de Estatística, Universidade de São Paulo, São Paulo, Brazil (Received 11 July 2006; final version received 3 July 2007) The generalized Birnbaum–Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum–Saunders models are compared by using this estimation method. Keywords: Elliptical distributions; Goodness-of-fit; Inverse Gaussian distribution; Monte Carlo simulation; Sinh-normal distribution Mathematics Subject Classification: Primary: 65C10; Secondary: 60E05 1. Introduction An important lifetime model originating from a material fatigue problem is the one derived by Birnbaum and Saunders [1]. The Birnbaum–Saunders (BS) distribution describes fatigue failure lifetimes. Due to its genesis, fatigue life and lifetime data in general are well modeled by this distribution. Outside the field of reliability, the BS distribution has been applied in a wide variety of fields. For details regarding old and new applications of the BS distribution, see [2, pp. 651–663; 3–8]. The BS distribution is defined in terms of the standard normal distribution and is related to the sinhyperbolic-normal (SHN) and inverse Gaussian (IG) distributions. Rieck and Nedelman [9] *Corresponding author. Email: victor.leiva@uv.cl; victor.leiva@yahoo.com Journal of Statistical Computation and Simulation ISSN 0094-9655 print/ISSN 1563-5163 online © 2008 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/00949650701550242