no. 3
The log-xgamma distribution with inference and application
[La distribution log-gamma : inférence et application]
Journal de la société française de statistique, Tome 159 (2018) no. 3, pp. 40-55.

Nous introduisons une nouvelle distribution à un paramètre sur l’intervalle [0, 1]. Ces principales caractéristiques (moments, moments censurés, fonction de survie) sont données, ainsi que d’autres caractérisations utiles. Les méthodes du maximum de vraisemblance, des moments et des moindres carrés sont présentés pour l’estimation de son paramètre. Les performances de ces estimateurs sont évaluées par des simulations de Monte-Carlo pour des échantillons de taille réduite. Une application à des données réelles est réalisée pour montrer l’intérêt de cette distribution par rapport aux distributions beta, de Kumaraswamy et de Topp-Leone.

In this paper, we introduce a new one-parameter distribution, called log-xgamma distribution, defined on the unit interval. Some of the statistical properties of the proposed distribution including moments, the incomplete moments and mean residual life function are obtained. Some useful characterization results of proposed distribution are presented. The maximum likelihood method, method of moments and least square estimation method are used to estimate the unknown parameter of the proposed model and finite sample performance of estimation methods are evaluated by means of Monte-Carlo simulation study. An application to the real data set is given to demonstrate the usefulness of the proposed distribution against the beta, the Kumaraswamy and the Topp-Leone distributions.

Keywords: Bounded distributions, Xgamma distribution, Characterization, Simulation
Mot clés : Distributions bornés, Distribution Xgamma, Caractérisation, Simulation 
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     title = {The log-xgamma distribution with inference and application},
     journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
     pages = {40--55},
     publisher = {Soci\'et\'e fran\c{c}aise de statistique},
     volume = {159},
     number = {3},
     year = {2018},
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     zbl = {1410.62021},
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     url = {http://www.numdam.org/item/JSFS_2018__159_3_40_0/}
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Altun, Emrah; Hamedani, GG. The log-xgamma distribution with inference and application. Journal de la société française de statistique, Tome 159 (2018) no. 3, pp. 40-55. http://www.numdam.org/item/JSFS_2018__159_3_40_0/

[1] Caramanis, M., Stremel, J., Fleck, W. and Daniel, S. (1983). Probabilistic production costing: an investigation of alternative algorithms. International Journal of Electrical Power and Energy Systems, 5(2), 75-86.

[2] Cordeiro, G. M. and de Castro, M. (2011). A new family of generalized distributions. Journal of statistical computation and simulation, 81(7), 883-898. | MR | Zbl

[3] Glänzel, W., A characterization theorem based on truncated moments and its application to some distribution families, Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Vol. B, Reidel, Dordrecht, 1987, 75–84. | MR | Zbl

[4] Glänzel, W. (1990). Some consequences of a characterization theorem based on truncated moments. Statistics: A Journal of Theoretical and Applied Statistics, 21(4), 613-618. | MR | Zbl

[5] Ghitany, M. E., Atieh, B. and Nadarajah, S. (2008). Lindley distribution and its application. Mathematics and computers in simulation, 78(4), 493-506. | MR | Zbl

[6] Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46(1-2), 79-88.

[7] Mazucheli, J., Menezes, A. F. and Dey, S. (2018). The unit-Birnbaum-Saunders distribution with applications. Chilean Journal of Statistics (ChJS), 9(1), 47-57. | MR

[8] Mazumdar, M. and Gaver, D. P. (1984). On the computation of power-generating system reliability indexes. Technometrics, 26(2), 173-185.

[9] Nadarajah, S. and Kotz, S. (2003). Moments of some J-shaped distributions. Journal of Applied Statistics, 30(3), 311-317. | MR | Zbl

[10] Papke, L. E. and Wooldridge, J. M. (1996). Econometric methods for fractional response variables with an application to 401 (k) plan participation rates. Journal of applied econometrics, 11(6), 619-632.

[11] Sen, S., Maiti, S. S. and Chandra, N. (2016). The Xgamma distribution: statistical properties and application. Journal of Modern Applied Statistical Methods, 15(1), 38.

[12] Sen, S., Chandra, N. and Maiti, S. S. (2017). The weighted xgamma distribution: properties and application. Journal of Reliability and Statistical Studies, 10(1).

[13] Sen, S. and Chandra, N (2017). The quasi xgamma distribution with application in bladder cancer data. Journal of Data Science, 15, 61-76.

[14] Topp, C. W. and Leone, F. C. (1955). A family of J-shaped frequency functions. Journal of the American Statistical Association, 50(269), 209-219. | MR | Zbl