An extended Birnbaum–Saunders model and its application in the study of environmental quality in Santiago, Chile

Abstract

In this article, we introduce, characterize and apply an extended version of the Birnbaum-Saunders model based on the Mudolkar-Hutson skew distribution. This model is appropriated for describing phenomena involving accumulation of some type, as is the case of environmental contamination. Specifically, we find the density, distribution function, and moments of the new model. In addition, we derive several properties and transformations related to this distribution. Furthermore, we propose an estimation method for the parameters of the model. Moreover, we conduct a study of its hazard rate focuses in environmental analysis. A computational implementation in R language of the obtained results is discussed. Finally, we present two examples with real data from environmental quality in Chile that illustrate the proposed methodology.

Monitoring Environmental Risk by a Methodology Based on Control Charts

“…651-663], and Fierro et al [9]. This is due to its good properties, its relation with the normal distribution and its applications in diverse fields including environmental sciences; see Leiva et al [16,17,19], Vilca et al [33,34], Ferreira et al [8], Marchant et al [25], and Saulo et al [32]. However, the most important aspect of the BS distribution is that it has physical arguments and statistical properties similar to the LN distribution to model this type of phenomena (e.g.…”

Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

“…The initial period contains few published papers reflecting the slow development of the methodology; see, for example, Birnbaum and Saunders (1969a); Rieck and Nedelman (1991); Johnson et al (1995); Dupuis and Mills (1998) and Owen and Padgett (1999). The second period (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010) includes papers that discuss varied aspects of estimation, modelling and diagnostics, as well as generalizations, computational issues and novel modelling examples, but with justifications still mainly based on an argument of cumulative effects; see, for example, Owen and Padgett (2000); Volodin and Dzhungurova (2000); Tsionas (2001); Rieck (2003); Galea et al (2004); Owen (2006); Xie and Wei (2007); Lemonte et al (2008); Leiva et al (2008Leiva et al ( , 2009); Balakrishnan et al (2009) and Vilca et al (2010). The third period (2011 to the present) is characterized by a new inventiveness, breaking the link with lifetime data analysis and hence extended application in new areas such as: biology, crop yield assessment, econometrics, energy production, forestry, industry, informatics, insurance, inventory management, medicine, psychology, neurology, pollution monitoring, quality control, sociology and seismology; see, for example, Bhatti (2010); Kotz et al (2010); Balakrishnan et al (2011); Leiva et al (2010Leiva et al ( , 2011Leiva et al ( , 2012; Vilca et al (2010); Villegas et al (2011); Azevedo et al (2012); Ferreira et al (2012);...…”

An Extension of the Birnbaum-Saunders Distribution Based on Skew-Normal t Distribution

“…The BS distribution is a popular model, commonly used in different areas of sciences and engineering; for example, Desmond (1985) considered the BS distribution as a model in biology, Leiva et al (2007), Barros et al (2008) presented some applications in the medical field, and Podlaski (2008), Leiva et al (2010) and Vilca et al (2010) used it to model data related to the forestry and environmental sciences.…”