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Title: The gamma-uniform distribution and its applications (English)
Author: Torabi, Hamzeh
Author: Montazeri Hedesh, Narges
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 48
Issue: 1
Year: 2012
Pages: 16-30
Summary lang: English
Category: math
Summary: Up to present for modelling and analyzing of random phenomenons, some statistical distributions are proposed. This paper considers a new general class of distributions, generated from the logit of the gamma random variable. A special case of this family is the Gamma-Uniform distribution. We derive expressions for the four moments, variance, skewness, kurtosis, Shannon and Rényi entropy of this distribution. We also discuss the asymptotic distribution of the extreme order statistics, simulation issues, estimation by method of maximum likelihood and the expected information matrix. We show that the Gamma-Uniform distribution provides great flexibility in modelling for negatively and positively skewed, convex-concave shape and reverse `J' shaped distributions. The usefulness of the new distribution is illustrated through two real data sets by showing that it is more flexible in analysing of the data than of the Beta Generalized-Exponential, Beta-Exponential, Beta-Pareto, Generalized Exponential, Exponential Poisson, Beta Generalized Half-Normal and Generalized Half-Normal distributions. (English)
Keyword: Bathtub shaped hazard rate function
Keyword: convex-concave shaped
Keyword: ExpIntegralE function
Keyword: regularized incomplete gamma function
Keyword: reverse ‘J’ shaped
Keyword: Shannon and Rényi entropy
MSC: 62A10
MSC: 93E12
idZBL: Zbl 1243.93123
idMR: MR2932926
Date available: 2012-03-05T08:26:46Z
Last updated: 2013-09-22
Stable URL:
Reference: [1] A. Akinsete, F. Famoye, C. Lee: The Beta-Pareto distribution..Statistics 42 (2008), 6, 547-563. MR 2465134, 10.1080/02331880801983876
Reference: [2] L. J. Bain, M. Engelhardt: Introduction to Probability and Mathematical Statistics..Second edition. Duxbury Press, Boston 1991, pp. 250–259. MR 0750654
Reference: [3] W. Barreto-Souza, A. H. S. Santos, G. M. Cordeirob: The Beta generalized exponential distribution..Statist. Comput. Simul. 80 (2010), 159-172. MR 2603623, 10.1080/00949650802552402
Reference: [4] K. Cooray, M. M. A. Ananda: A generalization of the half-normal distribution with applications to lifetime data..Comm. Statist. Theory Methods 37 (2008), 1323-1337. Zbl 1163.62006, MR 2526464, 10.1080/03610920701826088
Reference: [5] G. M. Cordeiro, A. J. Lemonte: The $\beta$-Birnbaum-Saunders distribution: An improved distribution for fatigue life modelling..Comput. Statist. Data Anal. 55 (2011), 1445-1461. MR 2741426, 10.1016/j.csda.2010.10.007
Reference: [6] G. M. Cordeiro, A. J. Lemonte: The beta Laplace distribution..Statist. Probab. Lett. 81 (2011), 973-982. Zbl 1221.60011, MR 2803732, 10.1016/j.spl.2011.01.017
Reference: [7] N. Eugene, C. Lee, F. Famoye: The Beta-Normal distribution and its applications..Commun. Statist. Theory Methods 31 (2002), 4, 497-512. MR 1902307, 10.1081/STA-120003130
Reference: [8] P. Feigl, M. Zelen: Estimation of exponential survival probabilities with concomitant information..Biometrics 21 (1965), 4, 826-838. 10.2307/2528247
Reference: [9] R. D. Gupta, D. Kundu: Generalized exponential distributions..Austral. and New Zealand J. Statist. 41 (1999), 2, 173-188. Zbl 1007.62503, MR 1705342, 10.1111/1467-842X.00072
Reference: [10] M. C. Jones: Families of distributions arising from distributions of order statistics..Test 13 (2004), 1, 1-43. Zbl 1110.62012, MR 2065642, 10.1007/BF02602999
Reference: [11] C. Kus: A new lifetime distribution..Comput. Statist. Data Anal. 51 (2007), 4497-4509. Zbl 1162.62309, MR 2364461, 10.1016/j.csda.2006.07.017
Reference: [12] C. Lee, F. Famoye, O. Olumolade: The Beta-Weibull distribution..J. Statist. Theory Appl. 4 (2005), 2, 121-136. MR 2210672
Reference: [13] S. Nadarajah, S. Kotz: The Beta Gumbel distribution..Math. Probl. Engrg. 10 (2004), 323-332. Zbl 1068.62012, MR 2109721, 10.1155/S1024123X04403068
Reference: [14] S. Nadarajah, S. Kotz: The Beta exponential distribution..Reliability Engrg. System Safety 91 (2006), 689-697. 10.1016/j.ress.2005.05.008
Reference: [15] S. Nadarajah, A. K. Gupta: The Beta Fréchet distribution..Far East J. Theor. Statist. 15 (2004), 15-24. Zbl 1074.62008, MR 2108090
Reference: [16] P. F. Paranaíba, E. M. M. Ortega, G. M. Cordeiro, R. R. Pescim, M. A. R. Pascoa: The Beta Burr XII distribution with applications to lifetime data..Comput. Statist. Data Anal. 55 (2011), 1118-1136. MR 2736499, 10.1016/j.csda.2010.09.009
Reference: [17] R. R. Pescim, C. G. B. Demétrio, G. M. Cordeiro, E. M. M. Ortega, M. R. Urbano: The Beta generalized half-Normal distribution..Comput. Statist. Data Anal. 54 (2009), 945-957. MR 2580929, 10.1016/j.csda.2009.10.007
Reference: [18] E. Mahmoudi: The beta generalized Pareto distribution with application to lifetime data..Math. Comput. Simul. 81 (2011), 11, 2414-2430. Zbl 1219.62024, MR 2811794, 10.1016/j.matcom.2011.03.006
Reference: [19] G. O. Silva, E. M. M. Ortega, G. M. Cordeiro: The beta modified Weibull distribution..Lifetime Data Anal. 16 (2010), 409-430. MR 2657898
Reference: [20] K. Zografos, S. Nadarajah: Expressions for Rényi and Shannon entropies for multivariate distributions..Statist. Probab. Lett. 71 (2005), 71-84. Zbl 1058.62008, MR 2125433, 10.1016/j.spl.2004.10.023


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