SEARCH WITHIN CONTENT
Citation Information : Statistics in Transition New Series. Volume 19, Issue 4, Pages 621-643, DOI: https://doi.org/10.21307/stattrans-2018-033
License : (CC BY-NC-ND 4.0)
Published Online: 15-March-2019
In this study, we introduce a new model called the Extended Exponentiated Power Lindley distribution which extends the Lindley distribution and has increasing, bathtub and upside down shapes for the hazard rate function. It also includes the power Lindley distribution as a special case. Several statistical properties of the distribution are explored, such as the density, hazard rate, survival, quantile functions, and moments. Estimation using the maximum likelihood method and inference on a random sample from this distribution are investigated. A simulation study is performed to compare the performance of the different parameter estimates in terms of bias and mean square error. We apply a real data set to illustrate the applicability of the new model. Empirical findings show that proposed model provides better fits than other well-known extensions of Lindley distributions.
AMROT, W., (2012). Estimation of Finite Population Kurtosis under Two-Phase Sampling for Nonresponse. Statistical Papers, 53, pp. 887–894.
GAMROT, W., (2013). Maximum Likelihood Estimation for Ordered Expectations of Correlated Binary Variables. Statistical Papers, 54, pp. 727–739.
KENNICKELL, A. B., (1997). Multiple Imputation and Disclosure Protection: The Case of the 1995 Survey of Consumer Finances. In Record Linkage Techniques. W. Alvey and B. Jamerson (eds.) Washington D. C.: National Academy Press, pp. 248–267.
SÄRNDAL, C-E., SWENSSON, B., WRETMAN, J., (1992). Model Assisted Survey Sam- ¨ pling, New York: Springer.
ALIZADEH, M., AFSHARI, M., HOSSEINI, B., RAMIRES, T. G, (2017). Extended ExpG family of distributions: Properties and Applications. Communication in statisticssimulation and computation, accepted.
ALIZADEH, M., ALTUN, E., OZEL, G., (2017). Odd Burr Power Lindley Distribution with Properties and Applications.Gazi University Journal of Science, Accepted.
AKINSETE, A. FAMOYE, F., LEE, C., (2008) The beta-Pareto distribution, A Journal of Theoretical and Applied Statistics Volume 42, Issue 6, pp. 547–563.
BAKOUCH, H. S., AL-MAHARANI, B. M., AL-SHOMRANI, A. A., MARCHI, V. A. A., LOUZADA, F., (2012): Anextended Lindley distribution, Journal of the Korean Statistical Society, Vol 41 (1), pp. 75– 85.
CAKMAKYAPAN, S., & OZEL, G., (2014). A new customer lifetime duration distribution: the Kumaraswamy Lindley distribution. International Journal of Trade, Economics and Finance, 5, 5, pp. 441–444.
CORDEIRO, G. M.,ALIZADEH, M., TAHIR, M. H., MANSOOR, M., BOURGUIGNON, M., & HAMEDANI, G. G., (2015). The beta odd log-logistic generalized family of distributions, Hacettepe Journal of Mathematics and Statistics, 45, 73, pp. 126-139.
GHITANY, M. E., ATIEH, B. & NADARAJAH, S., (2008). Lindley distribution and its application, Mathematics and Computers in Simulation, 78, pp. 493-506.
GHITANY, M. E., AL-MUTAIRI, D. K., BALAKRISHHNAN, N., & (2013). Al-Enezi, L. J. Power Lindley distribution and associated inference. Computational Statistics and Data Analysis, 64, pp. 20–33.
GLÄNZEL, W., , (1987). 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, pp. 75–84.
GLÄNZEL, W., (1990). Some consequences of a characterization theorem based on trun- ¨ cated moments, Statistics: A Journal of Theoretical and Applied Statistics, 21 (4), pp. 613–618.
GRADSHTEYN, I. S., RYZHIK, I. M., (2000). Table of integrals, series, and products. Academic Press, San Diego.
HAMEDANI, G. G., (2013). On certain generalized gamma convolution distributions II, Technical Report No. 484, MSCS, Marquette University
LEADBETTER, M. R., LINDGREN, G., ROOTZN H., (1983). Extremes and Related Properties of Random Sequences and Processes Springer Statist. Ser., Springer, Berlin.
LEHMANN E. L., CASELLA G., (1998). Theory of Point Estimation, Springer.
LINDLEY, D. V., (1958). Fiducial distributions and Bayesian theorem. Journal of the Royal Statistical Society B, 20, pp. 102–107.
MAZUCHELI, J., ACHCAR J. A., (2011). The Lindley Distribution Applied to Competing Risks Lifetime Data. Computer Methods and Programs in Biomedicine, 104(2), pp. 188-192.
NADARAJAH, S., BAKOUCH, H. S., & TAHMASBI, R., (2011). A generalized Lindley distribution. Sankhya B, 73, pp. 331-359.
OLUYEDE, B. O., YANG, T., & MAKUBATE, B., (2016). A new class of generalized power Lindley distribution with application to lifetime data. Asian Journal of Mathematics and Applications, 6, pp. 1-36.
RANJBAR, V., ALIZADEH, M., Alizade Morad Dr, Extended Generalized Lindley distribution: properties and applications. (Under review)
SHANKER, R., MISHRA, A., (2013). A quasi Lindley distribution, African Journal of Mathematics andComputer Science Research, Vol.6 (4), pp. 64-71.
SHARMA, V, SINGH, S., SINGH., U., & AGIWAL, V., (2015). The inverse Lindley distribution: a stress-strength reliability model with applications to head and neck cancer data. Journal of Industrial and Production Engineering, 32, 3, pp. 162–173.