An Epsilon Half Normal Slash Distribution and Its Applications to Nonnegative Measurements

Affiliation(s)

Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, USA.

Department of Management Science, National Chiao Tung University, HsinChu, Chinese Taipei.

Department of EPLS, Florida State University, Tallahassee, USA.

Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, USA.

Department of Management Science, National Chiao Tung University, HsinChu, Chinese Taipei.

Department of EPLS, Florida State University, Tallahassee, USA.

ABSTRACT

We introduce a new class of the slash distribution using the epsilon half normal distribution. The newly defined model extends the slashed half normal distribution and has more kurtosis than the ordinary half normal distribution. We study the characterization and properties including moments and some measures based on moments of this distribution. A simulation is conducted to investigate asymptotically the bias properties of the estimators for the parameters. We illustrate its use on a real data set by using maximum likelihood estimation.

Cite this paper

W. Gui, P. Chen and H. Wu, "An Epsilon Half Normal Slash Distribution and Its Applications to Nonnegative Measurements,"*Open Journal of Optimization*, Vol. 2 No. 1, 2013, pp. 1-8. doi: 10.4236/ojop.2013.21001.

W. Gui, P. Chen and H. Wu, "An Epsilon Half Normal Slash Distribution and Its Applications to Nonnegative Measurements,"

References

[1] L. Castro, H. Gómez and M. Valenzuela, “Epsilon Half-Normal Model: Properties and Inference,” Computational Statistics & Data Analysis, Vol. 56, No. 12, 2012, pp. 4338-4347. Hdoi:10.1016/j.csda.2012.03.020

[2] A. Pewsey, “Improved Likelihood Based Inference for the General Half-Normal Distribution,” Communications in Statistics—Theory and Methods, Vol. 33, No. 2, 2004, pp. 197-204. Hdoi:10.1081/STA-120028370

[3] N. Olmos, H. Varela, H. Gómez and H. Bolfarine, “An Extension of the Half-Normal Distribution,” Statistical Papers, Vol. 53, No. 4, 2011, pp. 1-12.

[4] M. Wiper, F. Girón and A. Pewsey, “Objective Bayesian Inference for the Half-Normal and Half-t Distributions,” Communications in Statistics—Theory and Methods, Vol. 37, No. 20, 2008, pp. 3165-3185. Hdoi:10.1080/03610920802105184

[5] W. Rogers and J. Tukey, “Understanding Some Long- Tailed Symmetrical Distributions,” Statistica Neerlandica, Vol. 26, No. 3, 1972, pp. 211-226. Hdoi:10.1111/j.1467-9574.1972.tb00191.x

[6] N. Johnson, S. Kotz and N. Balakrishnan, “Continuous Univariate Distributions,” Wiely, Hoboken, 1995.

[7] F. Mosteller and J. Tukey, “Data Analysis and Regression: A Second Course in Statistics,” Addison-Wesley Pub. Co., Boston, 1977.

[8] K. Kafadar, “A Biweight Approach to the One-Sample Problem,” Journal of the American Statistical Association, Vol. 77, No. 378, 1982, pp. 416-424. Hdoi:10.1080/01621459.1982.10477827

[9] H. Gómez, F. Quintana and F. Torres, “A New Family of Slash-Distributions with Elliptical Contours,” Statistics & Probability Letters, Vol. 77, No. 7, 2007, pp. 717-725. Hdoi:10.1016/j.spl.2006.11.006

[10] A. Genc, “A Generalization of the Univariate Slash by a Scale-Mixtured Exponential Power Distribution,” Communications in Statistics—Simulation and Computation, Vol. 36, No. 5, 2007, pp. 937-947. Hdoi:10.1080/03610910701539161

[11] J. Wang and M. Genton, “The Multivariate Skew-Slash Distribution,” Journal of Statistical Planning and Inference, Vol. 136, No. 1, 2006, pp. 209-220. Hdoi:10.1016/j.jspi.2004.06.023

[12] A. Azzalini, “A Class of Distributions Which Includes the Normal Ones,” Scandinavian Journal of Statistics, Vol. 12, No. 2, 1985, pp. 171-178.

[13] D. Andrews and A. Herzberg, “Data: A Collection of Problems from Many Fields for the Student and Research Worker,” Vol. 18, Springer-Verlag, New York, 1985.

[14] R. Barlow, R. Toland and T. Freeman, “A Bayesian Analysis of the Stress-Rupture Life of Kevlar/Epoxy Spherical Pressure Vessels,” In: C. Clarotti and D. Lindley, Eds., Accelerated Life Testing and Experts Opinions in Reliability, Elsevier Science Ltd., Amsterdam, 1988, pp. 203-236.

[1] L. Castro, H. Gómez and M. Valenzuela, “Epsilon Half-Normal Model: Properties and Inference,” Computational Statistics & Data Analysis, Vol. 56, No. 12, 2012, pp. 4338-4347. Hdoi:10.1016/j.csda.2012.03.020

[2] A. Pewsey, “Improved Likelihood Based Inference for the General Half-Normal Distribution,” Communications in Statistics—Theory and Methods, Vol. 33, No. 2, 2004, pp. 197-204. Hdoi:10.1081/STA-120028370

[3] N. Olmos, H. Varela, H. Gómez and H. Bolfarine, “An Extension of the Half-Normal Distribution,” Statistical Papers, Vol. 53, No. 4, 2011, pp. 1-12.

[4] M. Wiper, F. Girón and A. Pewsey, “Objective Bayesian Inference for the Half-Normal and Half-t Distributions,” Communications in Statistics—Theory and Methods, Vol. 37, No. 20, 2008, pp. 3165-3185. Hdoi:10.1080/03610920802105184

[5] W. Rogers and J. Tukey, “Understanding Some Long- Tailed Symmetrical Distributions,” Statistica Neerlandica, Vol. 26, No. 3, 1972, pp. 211-226. Hdoi:10.1111/j.1467-9574.1972.tb00191.x

[6] N. Johnson, S. Kotz and N. Balakrishnan, “Continuous Univariate Distributions,” Wiely, Hoboken, 1995.

[7] F. Mosteller and J. Tukey, “Data Analysis and Regression: A Second Course in Statistics,” Addison-Wesley Pub. Co., Boston, 1977.

[8] K. Kafadar, “A Biweight Approach to the One-Sample Problem,” Journal of the American Statistical Association, Vol. 77, No. 378, 1982, pp. 416-424. Hdoi:10.1080/01621459.1982.10477827

[9] H. Gómez, F. Quintana and F. Torres, “A New Family of Slash-Distributions with Elliptical Contours,” Statistics & Probability Letters, Vol. 77, No. 7, 2007, pp. 717-725. Hdoi:10.1016/j.spl.2006.11.006

[10] A. Genc, “A Generalization of the Univariate Slash by a Scale-Mixtured Exponential Power Distribution,” Communications in Statistics—Simulation and Computation, Vol. 36, No. 5, 2007, pp. 937-947. Hdoi:10.1080/03610910701539161

[11] J. Wang and M. Genton, “The Multivariate Skew-Slash Distribution,” Journal of Statistical Planning and Inference, Vol. 136, No. 1, 2006, pp. 209-220. Hdoi:10.1016/j.jspi.2004.06.023

[12] A. Azzalini, “A Class of Distributions Which Includes the Normal Ones,” Scandinavian Journal of Statistics, Vol. 12, No. 2, 1985, pp. 171-178.

[13] D. Andrews and A. Herzberg, “Data: A Collection of Problems from Many Fields for the Student and Research Worker,” Vol. 18, Springer-Verlag, New York, 1985.

[14] R. Barlow, R. Toland and T. Freeman, “A Bayesian Analysis of the Stress-Rupture Life of Kevlar/Epoxy Spherical Pressure Vessels,” In: C. Clarotti and D. Lindley, Eds., Accelerated Life Testing and Experts Opinions in Reliability, Elsevier Science Ltd., Amsterdam, 1988, pp. 203-236.