Keywords and phrases: generalization, likelihood ratio test, Lindley distribution, data analysis, failure rate, extended distributions
Received: May 26, 2024; Accepted: August 10, 2024; Published: December 13, 2024
How to cite this article: Alhassan Bunyaminu and Abukari Abdul-Lateef, Review of modifications of the Lindley distribution, Advances and Applications in Statistics 92(2) (2025), 231-272. https://doi.org/10.17654/0972361725012
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References: [1] M. V. Aarset, How to identify bathtub hazard rate, IEEE Transaction on Reliability 36 (1987), 106-108. [2] K. Adamidis and S. Loukas, A lifetime distribution with decreasing failure rate, Statistics and Probability Letters 39 (1998), 35-42. [3] A. Algarni, On a new generalized Lindley distribution: Properties, estimation and applications, PLoS ONE 16(2) (2021), e0244328. [4] A. Algarni, A. M. Almarashi, H. Okasha and H. K. T. Ng, E-Bayesian estimation of Chen distribution based on type-I censoring scheme, Entropy 22(6) (2020), 636. DOI: 10.3390/e22060636. [5] S. J. Almalki and S. Nadarajah, Modifications of the Weibull distribution: A review, Reliability Engineering and System Safety 124 (2014), 32-55. [6] W. A. H. Al-Nuaami, A. A. Heydari and H. J. Khamnei, The Poisson-Lindley distribution: some characteristics, with its application to SPC, Mathematics 11 (2023), 2428. [7] M. Z. Anis, Basic process capability indices: An expository review, International Statistical Review 76 (2008), 347-367. [8] A. Asgharzadeh, M. Alizadeh and M. Z. Raqab, Inverse Lindley distribution: different methods for estimating their PDF and CDF, Journal of Statistical Computation and Simulation 94(3) (2023), 604-623. DOI: 10.1080/00949655.2023.2265011. [9] E. Athayde, C. Azevedo, V. Leiva and S. A. Antonio, About the Birnbaum-Saunders distributions based on the Johnson system, Communications in Statistics: Theory and Methods 41(11) (2012), 2061-2079. [10] W. Barreto-Souza and H. S. Bakouch, A new lifetime model with decreasing failure rate, Journal of Theoretical and Applied Statistics 47(2) (2013), 465-476. [11] S. Basu, S. K. Singh and U. Singh, Estimation of inverse Lindley distribution using product of spacing function for hybrid censored data, Methodology and Computing in Applied Probability 21(2) (2019), 1377-1394. DOI: 10.1007/s11009-018-9676-6. [12] G. Casella and R. L. Berger, Statistical Inference, Duxbury Press, Belmont, CA, 1990. [13] S. Dey, F. A. Moala and D. Kumar, Statistical properties and different methods of estimation of Gompertz distribution with application, Journal of Statistical Management and Systems 21 (2018), 839-876. [14] I. Elbatal and M. Elgarhy, Transmuted quasi Lindley distribution: A generalization of the quasi Lindley distribution, International Journal of Pure and Applied Sciences and Technology 18 (2013), 59-70. [15] M. S. Eliwa, E. Altun, Z. A. Alhussain, E. A. Ahmed, M. M. Salah, H. H. Ahmed and M. El-Morshedy, A new one-parameter lifetime distribution and its regression model with applications, PLoS ONE 16(2) (2021), e0246969. https://doi.org/10.1371/journal.pone.024696. [16] M. El-Morshedy, M. S. Eliwa and H. Nagy, Exponentiated discrete Lindley distribution: Properties and applications, 2018. arXiv:1807.09895. [17] N. Eugene, C. Lee and F. Famoye, Beta-normal distribution and its applications, Communication and Statistics Theory and Methods 31 (2002), 497-512. [18] M. E. Ghitany, D. K. Al-Mutairi, N. Balakrishnan and L. J. Al-Enezi, Power Lindley distribution and associated inference, Computational Statistics and Data Analysis 64 (2013), 20-33. [19] M. E. Ghitany, B. Atieh and S. Nadarajah, Lindley distribution and its application, Mathematics Computing and Simulation 78 (2008), 493-506. [20] M. E. Ghitany, D. K. Al-Mutairi and S. Nadarajah, Zero-truncated Poisson-Lindley distribution and its application, Mathematics and Computers in Simulation 79 (2008), 279-287. [21] E. Gómez-Déniz and E. Calderín-Ojeda, The discrete Lindley distribution: properties and applications, Journal of Statistical Computation and Simulation 81(11) (2011), 1405-1416. [22] F. Gomes-Silva, A. Percontini, E. de Brito, M. W. Ramos, R. Venâncio and G. Cordeiro, The odd Lindley-G family of distributions, Austrian Journal of Statistics 46 (2017), 65-87. [23] W. Gu, S. Zhang and X. Lu, The Lindley-Poisson distribution in lifetime analysis and its properties, Hacettepe Journal of Mathematics and Statistics 43(6) (2014), 1063-1077. [24] P. K. Gupta and B. Singh, Parameter estimation of Lindley distribution with hybrid censored data, International Journal of System Assurance Engineering Management 4 (2013), 378-385. [25] N. L. Johnson, S. Kotz and N. Balakrishnan, Continuous Univariate Distributions, 2nd ed., Vol. 2, John Wiley & Sons Inc., New York, 1995. [26] H. Krishna and K. Kumar, Reliability estimation in Lindley distribution with progressively type II right censored sample, Mathematics and Computers in Simulation 82 (2011), 281-294. [27] C. Kus, M. C. Korkmaz, I. Kinaci, K. Karakaya and Y. Akdogan, Modified-Lindley distribution and its applications to the real data, Communications, Faculty of Science, University of Ankara Series, A1 Math. Stat. 71(1) (2022), 252-272. [28] M. T. Lai, Optimum number of minimal repairs for a system under increasing failure rate shock model with cumulative repair-cost limit, International Journal of Reliability and Safety 7 (2014), 95-107. [29] C. D. Lai, M. Xie and D. N. P. Murthy, A modified Weibull distribution, IEEE Transactions on Reliability 52(1) (2003), 33-37. [30] D. V. Lindley, Fiducial distributions and Bayes’ theorem, Journal of the Royal Statistical Society Series B 20 (1958), 102-107. [31] I. S. Mabrouk, Statistical inference for the parameter of the inverse Lindley distribution based on imprecise data with simulation study, International Journal of Contemporary Mathematical Sciences 14(4) (2019), 151-161. [32] B. Makubate, B. Oluyede and M. Gabanakgosi, A new Lindley-Burr XII distribution: Model, properties and applications, International Journal of Statistics and Probability 10(4) (2021), 33-51. [33] M. M. Mansour and S. M. Mohamed, A new generalized of transmuted Lindley distribution, Applied Mathematical Sciences 9 (2015), 2729-2748. [34] A. W. Marshall and I. A. Olkin, New method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84(3) (1997), 641-652. [35] J. Mazucheli and J. Achcar, The Lindley distribution applied to competing risks lifetime data, Computer Methods and Programs in Biomedicine 104 (2011), 188-192. [36] J. Mazucheli, A. F. B. Menezes and S. Chakraborty, On the one parameter unit-Lindley distribution and its associated regression model for proportion data, Journal of Applied Statistics 46(4) (2018), 700-714. DOI: 10.1080/02664763.2018.1511774. [37] F. Merovci, Transmuted Lindley distribution, International Journal of Open Problems in Computer Science and Mathematics 6 (2013), 63-72. [38] F. Merovci and E. Elbatal, Transmuted Lindley-geometric distribution and its applications, Journal of Statistics Applications and Probability 3 (2014), 77-91. [39] G. S. Mudholkar and D. K. Srivastava, Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability 42(2) (1993), 299-302. [40] S. Nadarajah, H. S. Bakouch and R. Tahmasbi, A generalized Lindley distribution, Sankhya B 73 (2011), 331-359. [41] B. O. Oluyede, T. Yang and B. Makubate, A new class of generalized power Lindley distribution with applications to lifetime data, Asian Journal of Mathematics and Applications 2016 (2016), Art. ID ama0279, 34pp. [42] M. Pararai, B. O. Oluyede and G. Warahena-Liyanage, The Beta Lindley-Poisson distribution with applications, Journal of Statistical and Econometric Methods 5(4) (2016), 1-37. [43] M. Pararai, B. O. Oluyede and G. Warahena-Liyanage, Kumaraswamy Lindley-Poisson Distribution: Theory and Applications, Asian Journal of Mathematics and Applications 2015 (2015), Art. ID ama0261, 30 pp. [44] M. Pararai, G. Warahena-Liyanage and B. O. Oluyede, A new class of generalized power Lindley distribution with applications to lifetime data, Theoretical Mathematics and Applications 5(1) (2015), 53-96. [45] F. A. Peña-Ramírez, R. R. Guerra and G. M. Cordeiro, The Nadarajah-Haghighi Lindley distribution, Annals of the Brazilian Academy of Sciences 91(1) (2019), e20170856. [46] A. Rashid, Z. Ahmad and T. R. Jan, Complementary compound Lindley power series distribution with application, Journal of Reliability and Statistical Studies 10(2) (2017), 143-158. [47] M. Sankaran, The discrete Poisson-Lindley distribution, Biometrics 26 (1970), 145-149. [48] R. Shanker and F. Hagos, On Poisson-Lindley distribution and its applications to biological Sciences, Biometrics and Biostatistics International Journal 2(4) (2015), 1-5. [49] R. Shanker and A. Mishra, A two-parameter Lindley distribution, Statistics in Transition New Series 14(1) (2013), 45-56. [50] R. Shanker and A. Mishra, A two-parameter Poisson-Lindley distribution, International Journal of Statistics and Systems 9(1) (2014), 79-85. [51] R. Shanker, K. K. Shukla, R. Shanker and T. K. Leonida, A three-parameter Lindley distribution, American Journal of Mathematics and Statistics 7(1) (2017), 15-26. [52] W. T. Shaw and I. R. C. Buckley, The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, 2007. arXiv:0901.0434 [53] U. Singh, P. K. Gupta and S. K. Upadhyay, Estimation of parameters for exponentiated-Weibull family under type-II censoring scheme, Computational Statistics and Data Analysis 48(3) (2005), 509-523. [54] V. Sharma, S. Singh, U. Singh and V. Agiwal, The inverse Lindley distribution: a stress-strength reliability model with applications to head and neck cancer data, Journal of Industrial Production and Engineering 32(3) (2015), 162-173. [55] M. H. Tahir, G. M. Cordeiro, A. Alzaatreh, M. Mansoor and M. Zubair, The logistic-X family of distributions and its applications, Communications in Statistics-Theory and Methods 45 (2016), 7326-7349. [56] L. Tomy, A retrospective study on Lindley distribution, Biometrics and Biostatistics International Journal 7(3) (2018), 163-169. [57] G. Warahena-Liyanage and M. Pararai, A generalized power Lindley distribution with applications, Asian Journal of Mathematics and Applications 2014 (2014), Art. ID ama0169, 23 pp. [58] H. Zakerzadeh and A. Dolati, Generalized Lindley distribution, Journal of Mathematical Extension 3(2) (2009), 1-17.
|