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Pinho, Luis Gustavo Bastos; Cordeiro, Gauss Moutinho; Nobre, Juvêncio Santos

On the Harris-G class of distributions: general results and application. (English) Zbl 1325.60010

Braz. J. Probab. Stat. 29, No. 4, 813-832 (2015).
Summary: We investigate some properties of the Harris-G class of distributions [E.-E. A. A. Aly and L. Benkherouf, Sankhyā, Ser. B 73, No. 1, 70–80 (2011; Zbl 1226.60019)]. We demonstrate that the density function of the Harris-G class can be expressed as a linear combination of density functions of the exponentiated baseline distribution. We provide general formulas for moments (raw, centered, incomplete and factorial), quantile function, generating functions and entropies. Two numerical examples are presented to demonstrate the potentiality of the models in this class. The first one applies the Harris-Burr XII distribution to model bimodal data. The second example uses the Harris-exponential distribution to model SAR image data. The results of the fitted models look promising.

Cited in 1 Document

MSC:

60E05 Probability distributions: general theory
60E10 Characteristic functions; other transforms
62E10 Characterization and structure theory of statistical distributions

Keywords:

Burr XII distribution; entropies; extended exponential distributions; Harris-G class; power series expansion

Citations:

Zbl 1226.60019
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Full Text: DOI Euclid

References:

[1] Aly, E. and Benkherouf, L. (2011). A new family of distributions based on probability generating functions. Sankhya B-Applied and Interdisciplinary Statistics 73 , 70-80. · Zbl 1226.60019 · doi:10.1007/s13571-011-0017-9
[2] Barreto-Souza, W. and Bakouch, H. S. (2013). A new lifetime model with decreasing failure rate. Statistics 47 , 465-476. · Zbl 1440.62357
[3] Chahkandi, M. and Ganjali, M. (2009). On some lifetime distributions with decreasing failure rate. Computational Statistics & Data Analysis 53 , 4433-4330. · Zbl 1298.62175 · doi:10.1016/j.csda.2009.06.016
[4] Chen, G. and Balakrishnan, N. (1995). A general purpose approximate goodness-of-fit test. Journal of Quality Technology 27 , 154-161.
[5] Cintra, R. J., Rêgo, L. C., Cordeiro, G. M. and Nascimento, A. D. C. (2014). Beta generalized normal distribution with an application for SAR image processing. Statistics 48 , 279-294. · Zbl 1294.60014 · doi:10.1080/02331888.2012.748776
[6] Cramér, H. (1946). Mathematical Methods of Statistics . Princeton: Princeton Univ. Press. · Zbl 0063.01014
[7] Frery, A. C., Müller, H. J., Yanasse, C. C. F. and Sant’Anna, S. J. S. (1997). A model for extremely heterogeneous clutter. IEEE Transactions on Geoscience and Remote Sensing 35 , 648-659.
[8] Gradshteyn, I. S. and Ryzhik, I. M. (2000). Table of Integrals, Series, and Products . San Diego: Academic Press. · Zbl 0981.65001
[9] Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica 50 , 1029-1054. · Zbl 0502.62098 · doi:10.2307/1912775
[10] Harris, T. E. (1948). Branching processes. The Annals of Mathematical Statistics 19 , 474-494. · Zbl 0041.45603 · doi:10.1214/aoms/1177730146
[11] Jaynes, E. T. (1957). Information theory and statistical mechanics. Physical Review 106 , 620-630. · Zbl 0084.43701 · doi:10.1103/PhysRev.106.620
[12] Kuş, C. (2006). A new lifetime distribution. Computational Statistics & Data Analysis 51 , 4497-4509. · Zbl 1162.62309 · doi:10.1016/j.csda.2006.07.017
[13] Lu, W. and Shi, D. (2012). A new compounding life distribution: The Weibull-Poisson distribution. Journal of Applied Statistics 39 , 21-38.
[14] Marshall, A. W. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84 , 641-652. · Zbl 0888.62012 · doi:10.1093/biomet/84.3.641
[15] Morais, A. L. and Barreto-Souza, W. (2011). A compound class of Weibull and power series distributions. Computational Statistics & Data Analysis 55 , 1410-1425. · Zbl 1328.62032 · doi:10.1016/j.csda.2010.09.030
[16] Pinho, L. G. B., Cordeiro, G. M. and Nobre, J. S. (2015). The Harris extended exponential distribution. Communications in Statistics: Theory and Methods 44 , 3486-3502. · Zbl 1328.62073 · doi:10.1080/03610926.2013.851221
[17] Ristić, M. and Nadarajah, S. (2012). A new lifetime distribution. Journal of Statistical Computation and Simulation 82 , 1191-1206. · Zbl 1297.62033
[18] Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal 27 , 379-432. · Zbl 1154.94303 · doi:10.1002/j.1538-7305.1948.tb01338.x
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