ARTICLE
ABSTRACT
In recent years, modifications of the classical Lindley distribution have been considered by many authors. In this paper, we introduce a new generalization of the Lindley distribution based on a mixture of exponential and gamma distributions with different mixing proportions and compare its performance with its sub-models. The new distribution accommodates the classical Lindley, Quasi Lindley, Two-parameter Lindley, Shanker, Lindley distribution with location parameter, and Three-parameter Lindley distributions as special cases. Various structural properties of the new distribution are discussed and the size-biased and the lengthbiased are derived. A simulation study is conducted to examine the mean square error for the parameters by means of the method of maximum likelihood. Finally, simulation studies and some real-world data sets are used to illustrate its flexibility in terms of its location, scale and shape parameters.
KEYWORDS
Lindley distribution, mixture distributions, size-biased distributions, maximum likelihood estimation
REFERENCES
BJERKEDAL, T., (1960). Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli, American Journal of Hygiene, 72(1), pp. 130–148.
FULLER, E. R., FREIMAN, S. W., QUINN, J. B., QUINN, G., CARTER, W., (1994). Fracture mechanics approach to the design of glass aircraft windows - A case study, Proceedings of SPIE - The International Society for Optical Engineering, pp. 419– 430.
GHITANY, M. E., ATIEH, B., NADARAJAH, S., (2008). Lindley distribution and its Applications, Mathematics and Computers in Simulation, 78(4), pp. 493–506.
GOVE, J. H., (2003a). Estimation and applications of size-biased distributions in forestry, Modeling forest systems. Edited by A. Amaro, D. Reed, and P. Soares. CABI Publishing, Walligford, UK., pp. 201–212.
GROSS, A. J., CLARK,V.A., (1975). Survival Distributions, Reliability Applications in the Biometrical Sciences, John Wiley, New York, USA.
HIBATULLAH, R., WIDYANINGSIH, Y., ABDULLAH, S., (2018). Marshall - Olkin extended power Lindley distribution with application, J. Ris. and Ap. Mat., 2(2), pp. 84 – 92.
LAWLESS, J. F., (1982). Statistical models and methods for lifetime data, John Wiley and Sons, New York, USA.
LINDLEY, D. V., (1958). Fiducial distributions and Bayes theorem, Journal of the Royal Statistical Society, Series B, 20(1), pp. 102–107.
LINDLEY, D. V., (1965). Introduction to Probability and Statistics from Bayesian viewpoint, part II, Inference, Cambridge university press, New York.
MONSEF, M. M. E. A., (2016). A new Lindley distribution with location parameter, Communications in Statistics-Theory and Methods, 45(17), pp. 5204–5219.
NICHOLS, M. D., PADGETT, W. J., (2006). A bootstrap control chart for Weibull percentiles, Quality and Reliability Engineering International, 22(2), pp. 141–151.
RENYI, A. (1961). On measures of entropy and information, In Fourth Berkeley Symposium on Mathematical Statistics and Probability, pp. 547–561.
SHANKER, R., MISHR, A., (2013a). A Quasi Lindley Distribution, African Journal of Mathematics and Computer Science Research, 6(4), pp. 64 –71.
SHANKER, R., MISHR, A., (2013b). A two-parameter Lindley distribution, Statistics in Transition new Series, 14(1), pp. 45–56.
SHANKER, R., SHARMA, S., SHANKER, R., (2013). A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data, Applied Mathematics, 4, pp. 363–368.
SHANKER, R., (2015). Shanker Distribution and Its Applications, International Journal of Statistics and Applications, 5(6), pp. 338–348.
SHANKER, R., SHUKLA, K. K., SHANKER, R., TEKIE, A. L., (2017). A Threeparameter Lindley Distribution, American Journal of Mathematics and Statistics, 7(1), pp. 15–26.
SHANNON, C., WEAVER, W., (1949). The mathematical theory of communication, Chicago: University of Illinois Press.
