Applicationsshow that the new family of distributions can provide a better fitthan several existing lifetime models.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this paper, we propose a new class of distributions called the Lindleygenerator with one extra parameter to generate many continuous distributions.The new distribution contains several distributions as submodels,such as Lindley-Exponential, Lindley-Weibull, and LindleyLomax.Some mathematical properties of the new generator, includingordinary moments, quantile and generating functions, limiting behaviors,some entropy measures and order statistics, which hold for anybaseline model, are presented.
📊
Key Findings & Data:The importance of thenew generator is illustrated by means of three real data sets.
💡
Conclusion & Impact:Applicationsshow that the new family of distributions can provide a better fitthan several existing lifetime models.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, we propose a new class of distributions called the Lindleygenerator with one extra parameter to generate many continuous distributions.The new distribution contains several distributions as submodels,such as Lindley-Exponential, Lindley-Weibull, and LindleyLomax.Some mathematical properties of the new generator, includingordinary moments, quantile and generating functions, limiting behaviors,some entropy measures and order statistics, which hold for anybaseline model, are presented. Then, we discuss the maximum likelihoodmethod to estimate model parameters. The importance of thenew generator is illustrated by means of three real data sets. Applicationsshow that the new family of distributions can provide a better fitthan several existing lifetime models.
🔖
Cite This Article
ÖZEL, G., CAKMAKYAPAN, S. (2022). The Lindley family of distributions: properties and applications ∗† and Gamze Ozel‡. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 6, 1113–1137. https://ajindex.com/articles/529992
T. Banerjee, S.B. Singh and R.K. Srivastava, Development and performance evaluation of statistical models correlating air pollutants and meteorological variables at Pantnagar, India Atmos Res 99 505-517, (2011).
E.E. Ukpebor, S.I. Ahonkhal and H. Heydtman, NO2 measurement with passive sampler: assessment of the sensitivity of two types of palmes diffusion tubes for NO2, Intern J Environ Studies 61, 67-71, (2004).
A. Akdemir, The creation of pollution mapping and measurement of ambient concentration of sulfur dioxide and nitrogen dioxide with passive sampler, J Environ Health Sci Eng 12, (2014).
G. Ozel and S. Cakmakyapan, A new approach to the prediction of PM10 concentrations in Central Anatolia Region, Turkey, Atmos Pollut Res 6, 735-741, (2015).
J.A. Doornik, Ox 5: An Object-Oriented Matrix Programming Language, Timberlake Consultants, London, 2007.
C.E. Shannon, Prediction and entropy of printed English, Bell Syst Tech J 30, 50-64, (1951).
A. Renyi, On measures of entropy and information, In: Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, 547-561.
University of California Press, Berkeley, 1961.
S. Nadarajah, G.M. Cordeiro, and E. M. Ortega, General results for the Kumaraswamy-G distribution, J Stat Comput Sim 82 951-979, (2012).
A.J. Lemonte, W. Barreto-Souza and G.M. Cordeiro, The exponentiated Kumaraswamy distribution and its log-transform, Braz J Probab Statist 27 31-53, (2013).
S. Nadarajah, G.M. Cordeiro and E.M.M. Ortega, General results for the Kumaraswamy-G distribution, J Stat Comput Sim, 951-972, (2012). P.F. Parana’ıba, E.M.M. Ortega, G.M. Cordeiro and M.A.R. Pascoa, The Kumaraswamy Burr XII distribution: theory and practice, J Stat Comput Sim 82, 1–27, (2012).
M.A.R. Pascoa, E.M.M. Ortega, and G.M. Cordeiro, The Kumaraswamy generalized gamma distribution with application in survival analysis, Statist Methodol 8, 411–433, (2011).
G.M. Cordeiro, S. Nadarajah and E.M.M. Ortega, The Kumaraswamy Gumbel distribution, Statist Meth Applic 21, 139-168, (2012).
S. Nadarajah and A.K. Gupta, A generalized gamma distribution with application to drought data, Math Comput Simulat 74, 1-7, (2007).
R.D. Gupta and D. Kundu, Generalized Exponential Distributions: Different Methods of Estimation, J Stat Comput Sim 69, 315-338, (2001).
R.D. Gupta and D. Kundu, Exponentiated Exponential Family; An Alternative to Gamma and Weibull, Biometrical J 33, 117-130, (2001).
R D. Gupta and D. Kundu, Generalized Exponential Distributi