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},
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     volume = {159},
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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/

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