A Skewed Sinh-Normal Distribution and Its Properties and Application to Air Pollution

In this article, we introduce a skewed version of the sinh-normal distribution and discuss some of its properties. In addition, we characterize an extension of the Birnbaum–Saunders model associated with this distribution from a probabilistic viewpoint along with a lifetime analysis based on its hazard rate. Finally, one of the proposed models is applied to air pollution data in order to illustrate its usefulness.

[1]  J. Bert Keats,et al.  Statistical Methods for Reliability Data , 1999 .

[2]  Narayanaswamy Balakrishnan,et al.  Lifetime analysis based on the generalized Birnbaum-Saunders distribution , 2008, Comput. Stat. Data Anal..

[3]  Dong Shang Chang,et al.  Reliability bounds and critical time for the Birnbaum-Saunders distribution , 1993 .

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

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

[6]  N. L. Johnson,et al.  Systems of frequency curves generated by methods of translation. , 1949, Biometrika.

[7]  Mukesh Khare,et al.  Statistical behavior of carbon monoxide from vehicular exhausts in urban environments , 2007, Environ. Model. Softw..

[8]  Gilberto A. Paula,et al.  Influence diagnostics in log-Birnbaum-Saunders regression models with censored data , 2007, Comput. Stat. Data Anal..

[9]  George Christakos,et al.  An extended Birnbaum–Saunders model and its application in the study of environmental quality in Santiago, Chile , 2010 .

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

[11]  Mukesh Khare,et al.  A Review of Deterministic, Stochastic and Hybrid Vehicular Exhaust Emission Models , 2004 .

[12]  A. Basu,et al.  The Inverse Gaussian Distribution , 1993 .

[13]  James R. Rieck,et al.  Parameter estimation for ihe birnbaum-saunders distribution based on symmetrically censored samples , 1995 .

[14]  L Wang,et al.  Statistical analysis for the Birnbaum-Saunders fatigue life distribution under censored testing , 1996 .

[15]  Saralees Nadarajah,et al.  A truncated inverted beta distribution with application to air pollution data , 2008 .

[16]  James R. Rieck,et al.  A log-linear model for the Birnbaum-Saunders distribution , 1991 .

[17]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[18]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[19]  F. Famoye.  Continuous Univariate Distributions, Volume 1 , 1994 .

[20]  B. Dhillon.  Life Distributions , 1981, IEEE Transactions on Reliability.

[21]  Sam C. Saunders.  A Family of Random Variables Closed Under Reciprocation , 1974 .

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

[23]  Narayanaswamy Balakrishnan,et al.  Mixture inverse Gaussian distributions and its transformations, moments and applications , 2009 .

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

[25]  Gilberto A. Paula,et al.  Influence Diagnostics in log-Birnbaum-Saunders Regression Models , 2004 .

[26]  Ronald Christensen,et al.  Log-Linear Models and Logistic Regression , 1997 .

[27]  A. Azzalini.  A class of distributions which includes the normal ones , 1985 .

[28]  R. Berk,et al.  Continuous Univariate Distributions, Volume 2 , 1995 .

[29]  S. Kotz,et al.  Survey of developments in the theory of continuous skewed distributions , 2005 .

[30]  Filidor Vilca-Labra,et al.  A New Fatigue Life Model Based on the Family of Skew-Elliptical Distributions , 2006 .

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

[32]  James R. Rieck,et al.  A Comparison of Two Random Number Generators for the Birnbaum–Saunders Distribution , 2003 .

[33]  Narayanaswamy Balakrishnan,et al.  The Generalized Birnbaum–Saunders Distribution and Its Theory, Methodology, and Application , 2008 .

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

[35]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

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