ON ESTIMATING PARAMETERS OF LINDLEY-GEOMETRIC DISTRIBUTION

Year 2021, Volume: 22 Issue: 2, 160 - 167, 29.06.2021

Caner Tanış , Kadir Karakaya

https://doi.org/10.18038/estubtda.816836

Cited By: 1

Abstract

Lindley-geometric (LG) distribution is generated by compounding Lindley and geometric distribution. We tackle the problem of estimating parameters for LG distribution. For this purpose maximum likelihood, least-squares, weighted least-squares, Anderson-Darling and Crámer–von-Mises are used in order to estimate the two parameters of LG distribution. We also consider an extensive Monte Carlo simulation study to evaluate these methods according to the biases and mean-squared errors (MSEs). Finally, eight real data applications are presented.

Keywords

Estimation of parameter, Geometric distribution, Lindley distribution, Lindley-geometric distribution, Monte Carlo simulation

References

• Mazucheli J, Louzada F, Ghitany, ME. Comparison of estimation methods for the parameters of the weighted Lindley distribution. Applied Mathematics and Computation 2013; 220: 463-471.
• Gupta PK, Singh, B. Parameter estimation of Lindley distribution with hybrid censored data. International Journal of System Assurance Engineering and Management 2013; 4: 378-385.
• Singh SK, Singh U, Sharma VK. Bayesian estimation and prediction for the generalized Lindley distribution under asymmetric loss function. Hacettepe Journal of Mathematics and Statistics 2014; 43: 661-678.
• Al-Zahrani B, Gindwan M. Parameter estimation of a two-parameter Lindley distribution under hybrid censoring. International Journal of System Assurance Engineering and Management 2014; 5: 628-636.
• Santo APJ, Mazucheli J. Comparison of estimation methods for the Marshall–Olkin extended Lindley distribution. Journal of Statistical Computation and Simulation 2015; 85: 3437-3450.
• Gui W, Chen M. Parameter estimation and joint confidence regions for the parameters of the generalized Lindley distribution. Mathematical Problems in Engineering 2016; Avaible at http://dx.doi.org/10.1155/2016/7946828.
• Zakerzadeh H, Mahmoudi E. A new two parameter lifetime distribution: model and properties. 2012; arXiv preprint arXiv:1204.4248.
• Warahena-Liyanage G, Pararai M. The Lindley power series class of distributions: Model, properties and applications. Journal of Computations and Modelling 2015; 5: 35-80.
• Merovci F. Elbatal I. Transmuted Lindley-geometric distribution and its applications. Journal of Statistics Applications and Probability 2013; 3: 77-91.
• Diab LS, Muhammed HZ. Quasi Lindley Geometric Distribution. International Journal of Computer Applications 2014; 95: 9-16.
• Gui W, Zhang H, Guo L. The Complementary Lindley-Geometric Distribution and Its Application in Lifetime Analysis. Sankhya B 2017; 79: 316-335.
• Elbatal I, Khalil MG. A New Extension of Lindley Geometric Distribution and its Applications. Pakistan Journal of Statistics and Operation Research 2019; 15: 249-263.
• Mudholkar GS, Srivastava DK, Freimer M. The exponentiated Weibull family: A reanalysis of the bus-motor-failure data. Technometrics 1995; 37: 436-445.
• Andrews DF, Herzberg AM. Data: A Collection of Problems from Many Fields for the Student and Research Worker 1985; New York: Springer Series in Statistics.
• Jorgensen B. Statistical Properties of the Generalized Inverse Gaussian distribution. 2012; 9: Springer Science and Business Media.
• Lawless JF. Statistical Models and Methods for Lifetime Data. 2003; Wiley: New York.
• Murthy D, Xie M, Jiang R. Weibull models. John Wiley and Sons 2004; 505: 180.
• Bhaumik DK, Kapur KG, Gibbons RD. Testing parameters of a gamma distribution for small samples. Technometrics 2009; 51: 326-334.
• Nadarajah S. A truncated inverted beta distribution with application to air pollution data. Stochastic Environmental Research and Risk 2008; 22: 285–289.
• Leiva V, Vilca F, Balakrishnan N, Sanhueza A. A skewed sinh-normal distribution and its properties and applicati to air pollution. Communications in Statistics-Theory and Methods 2010; 39: 426–443.
• Bekker A, Roux JJJ, Mosteit PJ. A generalization of the compound Rayleigh distribution: using a Bayesian method on cancer survival times. Communications in Statistics-Theory and Methods 2000; 29: 1419-1433.