New Extended Generalized Lindley Distribution: Properties and Applications
Keywords:Lindley distribution, Mathai-Haubold entropy, Maximum likelihood estimation, Asymptotic confidence interval, Likelihood ratio test
In this paper, we introduce a new extended generalized Lindley distribution ($NEGLD$). Some statistical properties of the proposed distribution are explicitly derived. These include conditional moments, vitality function, geometric vitality function, mean inactivity time and various entropy measures. Maximum likelihood estimation, moment estimation and asymptotic confidence interval are used for estimating the parameters. The distribution has been fitted to a data set to test its goodness of fit and it has been found that this distribution gives better fit than the some other well-known existing distributions.
A. M. ABOUAMMOH, A. M. ALSHANGITI, I. E. RAGAB (2015). A new generalized Lindley distribution. Journal of Statistical Computation and Simulation, 85(18): 3662–3678.
S. ALI, M. ASLAM, S. M. KAZMI (2013). A study of the effect of the loss function on Bayes Estimate posterior risk and hazard function for Lindley distribution. Appl Math Model, 37: 6068–6078.
T. BJERKEDAL (1960). Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. American Journal of Hygiene, 72: 130–148.
A. DI CRESCENZO, M. LONGOBARDI (2002). Entropy-based measure of uncertainty in past life-time distributions. Journal of Applied Probability, 39(2): 434–440.
N. EBRAHIMI (1996). How to measure uncertainty in the residual life-time distribution. Sankhy¯a A, 58(1): 48–56.
N. EBRAHIMI, F. PELLEREY (1995). New partial ordering of survival functions based on the notion of uncertainty. Journal of Applied Probability, 32(1): 202–211.
I. ELBATAL, M. ELGARHY (2013). Transmuted quasi Lindley distribution: a generalization of the quasi Lindley distribution. Int J Pure Appl Sci Technol, 18: 59–70.
M. E. GHITANY, B. ATIEH, S. NADARAJAH (2008). Lindley distribution and its applications. Mathematics and Computers in Simulation, 78(4): 493–506.
M. E. GHITANY, D. K. AL-MUTAIRI, N. BALAKRISHNAN, L. J. AL-ENEZI (2013), Power Lindley distribution and associated inference. Computational Statistics and Data Analysis, 64: 20–33.
D. E. GOMEZ, E. C. OJEDA (2011). The discrete Lindley distribution: Properties and applications. Journal of Statistical Computation and Simulation, 81(11): 1405–1416.
G. O. KADILAR, S. CAKMAKYAPAN (2016). The Lindley family of distributions: Properties and applications. Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics.
D. V. LINDLEY (1958). Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society, Series B, 20(1): 102–107.
A. M. MATHAI, H. J. HAUBOLD (2006). Pathway models, Tsallis statistics, superstatistics and a generalized measure of entropy. Physics A, 375: 110–122.
M. M. E. A. MONSEF (2015). A new Lindley distribution with location parameter. Communications in Statistics-Theory and Methods(online).
S. NADARAJAH, H. BAKOUCH R. TAHMASBI (2011). A generalized lindley distribution. Sankhya B - Applied and Interdisciplinary Statistics, 73: 331–359.
S. NEDJAR, H. ZEHDOUDI (2016). On gamma Lindley distribution: Properties and simulations. Journal of Computational and Applied Mathematics, 298: 167–174.
M. SANKARAN (1970): The discrete Poisson-Lindley distribution. Biometrics, 26: 145–149.
R. SHANKER, S. SHARMA, R. SHANKER (2013). A two-parameter Lindley distribution for modeling waiting and survival times data. Applied Mathematics, 4: 363–368.
C. E. SHANNON (1948). A Mathematical theory of communication. The Bell System Technical Journal, 27: 379–423 and 623–656.
B. D. SHARMA, D. P. MITTAL (1977). New non-additive measures of relative information. Journal of Combinatorics Information and System Sciences, 2(4): 122–132.
H. ZAKERZADEH, A. DOLATI (2009). Generalized Lindley distribution. Journal of Mathematical Extension, 3(2): 13–25.