Abstract
In this paper we introduce an extension of the half-normal distribution in order to model a great variety of non-negative data. Its hazard rate function can be decreasing or increasing, depending on its parameters. Some properties of this new distribution are presented. For example, we give a general expression for the moments and a stochastic representation. Also, the cumulative distribution function, the hazard rate function, the survival function and the quantile function can be easily evaluated. Maximum likelihood estimators can be computed by using numerical procedures. Finally, a real-life dataset has been presented to illustrate its applicability.
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References
H Akaike. A new look at the statistical model identification, IEEE Trans Automat Control, 1974, 19(6): 716–723.
D F Andrews, A M Herzberg. Data: A Collection of Problems from Many Fields for the Student and Research Worker, Springer Series in Statistics, New York, 1985.
R E Barlow, R H Toland, T Freeman. A Bayesian analysis of stress-rupture life of kevlar 49/epoxy spherical pressure vessels, In: Proc Canad Conf Appl Statist, Marcel Dekker, New York, 1984.
H Bozdogan. Model selection and Akaike’s Information Criterion (AIC): The general theory and its analytical extensions, Psychometrika, 1987, 52: 345–370.
C Y Chou, H R Liu. Properties of the half-normal distribution and its application to quality control, J Ind Technol, 1998, 14(3): 4–7.
K Cooray, M M A Ananda. A generalization of the half-normal distribution with applications to lifetime data, Comm Statist Theory Methods, 2008, 37: 1323–1337.
G M Cordeiro, R R Pescim, E M M Ortega. The Kumaraswamy generalized half-normal distribution for skewed positive data, J Data Sci, 2012, 10: 195–224.
W Gander, W Gautschi. Adaptive Quadrature — Revisited, BIT, 2000, 40: 84–101.
D P Murthy, M Xie, R Jiang. Weibull Models, Wiley Series in Probability and Statistics, Vol 505, John Wiley & Sons, 2004.
S Nadarajah, F Haghighi. An extension of the exponential distribution, Statistics, 2011, 45(6): 543–558.
M A Khan, H M Islam. Bayesian analysis of system availability with half-normal life time, Qual Technol Quant Manag, 2012, 9(2): 203–209.
N M Olmos, H Varela, H W Gómez, H Bolfarine. An extension of the half-normal distribution, Statist Papers, 2012, 53: 875–886.
A Pewsey. Large-sample inference for the general half-normal distribution, Comm Statist Theory Methods, 2002, 31: 1045–1054.
A Pewsey. Improved likelihood based inference for the general half-normal distribution, Comm Statist Theory Methods, 2004, 33(2): 197–204.
G Schwarz. Estimating the dimension of a model, Ann Statist, 1978, 6: 461–464.
M P Wiper, F J Girón, A Pewsey. Objective Bayesian inference for the half-normal and half-t distributions, Comm Statist Theory Methods, 2008, 37: 3165–3185.
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The first author was supported by Becas-Chile of the Chilean government and the second author was supported by Grant FONDECYT 1130375.
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Gómez, Y.M., Vidal, I. A generalization of the half-normal distribution. Appl. Math. J. Chin. Univ. 31, 409–424 (2016). https://doi.org/10.1007/s11766-016-3366-3
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DOI: https://doi.org/10.1007/s11766-016-3366-3