The Kumaraswamy-geometric distribution. (English) Zbl 1357.62068
Summary: In this paper, the Kumaraswamy-geometric distribution, which is a member of the \(T\)-geometric family of discrete distributions is defined and studied. Some properties of the distribution such as moments, probability generating function, hazard and quantile functions are studied. The method of maximum likelihood estimation is proposed for estimating the model parameters. Two real data sets are used to illustrate the applications of the Kumaraswamy-geometric distribution.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 62F10 | Point estimation |
| 62P20 | Applications of statistics to economics |
| 60E05 | Probability distributions: general theory |
References:
| [1] | Akinsete, A, Famoye, F, Lee, C: The beta-Pareto distributions. Statistics. 42(6), 547-563 (2008). · Zbl 1274.60033 · doi:10.1080/02331880801983876 |
| [2] | Alexander, C, Cordeiro, GM, Ortega, EMM, Sarabia, JM: Generalized beta-generated distributions. Comput. Stat. Data Anal. 56, 1880-1897 (2012). · Zbl 1245.60015 · doi:10.1016/j.csda.2011.11.015 |
| [3] | Alshawarbeh, E, Famoye, F, Lee, C: Beta-Cauchy distribution: some properties and its applications. J. Stat. Theory Appl. 12, 378-391 (2013). · doi:10.2991/jsta.2013.12.4.5 |
| [4] | Alzaatreh, A, Famoye, F, Lee, C: Gamma-Pareto distribution and its applications. J. Mod. Appl. Stat. Meth. 11(1), 78-94 (2012a). |
| [5] | Alzaatreh, A, Famoye, F, Lee, C: Weibull-Pareto distribution and its applications. Comm. Stat. Theor. Meth. 42(7), 1673-1691 (2013a). · Zbl 1294.62017 · doi:10.1080/03610926.2011.599002 |
| [6] | Alzaatreh, A, Lee, C, Famoye, F: On the discrete analogues of continuous distributions. Stat. Meth. 9, 589-603 (2012b). · Zbl 1365.62059 · doi:10.1016/j.stamet.2012.03.003 |
| [7] | Alzaatreh, A, Lee, C, Famoye, F: A new method for generating families of continuous distributions. Metron. 71, 63-79 (2013b). · Zbl 1302.62026 · doi:10.1007/s40300-013-0007-y |
| [8] | Arbous, AG, Sichel, HS: New techniques for the analysis of asenteeism data. Biometrika. 41, 77-90 (1954). · Zbl 0055.13711 · doi:10.1093/biomet/41.1-2.77 |
| [9] | Chatfield, C: A marketing application of characterization theorem. In: Patil, GP, Kotz, S, Ord, JK (eds.)Statistical Distributions in Scientific Work, volume 2, pp. 175-185. D. Reidel Publishing Company, Boston (1975). · Zbl 1068.62012 |
| [10] | Consul, PC: Generalized Poisson Distributions: Properties and Applications. Marcel Dekker, Inc., New York (1989). · Zbl 0691.62015 |
| [11] | Consul, PC, Famoye, F: Lagrangian Probability Distributions. Birkhäuser, Boston (2006). · Zbl 1103.62013 |
| [12] | Cordeiro, GM, de Castro, M: A new family of generalized distributions. J. Stat. Comput. Simulat. 81(7), 883-898 (2011). · Zbl 1219.62022 · doi:10.1080/00949650903530745 |
| [13] | Cordeiro, GM, Lemonte, AJ: The beta Laplace distribution. Stat. Probability Lett. 81, 973-982 (2011). · Zbl 1221.60011 · doi:10.1016/j.spl.2011.01.017 |
| [14] | Cordeiro, GM, Nadarajah, S, Ortega, EMM: The Kumaraswamy Gumbel distribution. Stat. Methods Appl. 21, 139-168 (2012). · doi:10.1007/s10260-011-0183-y |
| [15] | de Pascoa, MAR, Ortega, EMM, Cordeiro, GM: The Kumaraswamy generalized gamma distribution with application in survival analysis. Stat. Meth. 8, 411-433 (2011). · Zbl 1219.62026 · doi:10.1016/j.stamet.2011.04.001 |
| [16] | de Santana, TV, Ortega, EMM, Cordeiro, GM, Silva, GO: The Kumaraswamy-log-logistic distribution. Stat. Theory Appl. 3, 265-291 (2012). |
| [17] | Eugene, N, Lee, C, Famoye, F: The beta-normal distribution and its applications. Comm. Stat. Theor. Meth. 31(4), 497-512 (2002). · Zbl 1009.62516 · doi:10.1081/STA-120003130 |
| [18] | Famoye, F, Lee, C, Olumolade, O: The beta-Weibull distribution. J. Stat. Theory Appl. 4(2), 121-136 (2005). |
| [19] | Gupta, RC, Ong, SD: A new generalization of the negative binomial distribution. Comput. Stat. Data Anal. 45, 287-300 (2004). · Zbl 1430.62036 · doi:10.1016/S0167-9473(02)00301-8 |
| [20] | Jain, GC, Consul, PC: A generalized negative binomial distribution. SIAM J. Appl. Math. 21, 501-513 (1971). · Zbl 0234.60010 · doi:10.1137/0121056 |
| [21] | Johnson, NL, Kemp, AW, Kotz, S: Univariate Discrete Distributiuons. third edition. John Wiley & Sons, New York (2005). · Zbl 1092.62010 · doi:10.1002/0471715816 |
| [22] | Jones, MC: Kumaraswamy’s distribution: a beta-type distribution with some tractability advantages. Stat. Methodologies. 6, 70-81 (2009). · Zbl 1215.60010 · doi:10.1016/j.stamet.2008.04.001 |
| [23] | Kong, L, Lee, C, Sepanski, JH: On the properties of of beta-gamma distribution. J. Mod. Appl. Stat. Meth. 6(1), 187-211 (2007). |
| [24] | Kumaraswamy, P: A generalized probability density function for double-bounded random processes. Hydrology 46, 79-88 (1980). · doi:10.1016/0022-1694(80)90036-0 |
| [25] | Lemonte, AJ, Barreto-Souza, W, Cordeiro, GM: The exponentiated Kumaraswamy distribution and its log-transform. Braz. J. Probability Stat. 27, 31-53 (2013). · Zbl 1319.62032 · doi:10.1214/11-BJPS149 |
| [26] | Mahmoudi, E: The beta generalized Pareto distribution with application to lifetime data. Math. Comput. Simulations. 81, 2414-2430 (2011). · Zbl 1219.62024 · doi:10.1016/j.matcom.2011.03.006 |
| [27] | Nadarajah, S, Kotz, S: The beta Gumbel distribution. Math. Probl. Eng. 2004(4), 323-332 (2004). · Zbl 1068.62012 · doi:10.1155/S1024123X04403068 |
| [28] | Nadarajah, S, Kotz, S: The beta exponential distribution. Reliability Eng. Syst. Saf. 91, 689-697 (2006). · doi:10.1016/j.ress.2005.05.008 |
| [29] | Singla, N, Jain, K, Sharma, SK: The beta generalized Weibull distribution: properties and applications. Reliability Eng. Syst. Saf. 102, 5-15 (2012). · doi:10.1016/j.ress.2012.02.003 |
| [30] | Zwillinger, D, Kokoska, S: Standard Probability and Statistics Tables and Formulae. Chapman and Hall/CRC, Boca Raton (2000). · Zbl 0943.62124 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
