Testing the Validity of Lindley Model Based on Informational Energy with Application to Real Medical Data

  • Hadi Alizadeh Noughabi University of Birjand, Iran
Keywords: Lindley distribution;, Informational energy, Test of fit, Power of test, Monte Carlo simulation


In this article, a test statistic for testing the validity of the Lindley model based on the informational energy is proposed. Consistency of our test is shown. Through a simulation study, we obtain the critical values of the test statistic and then the power of the test is computed by Monte Carlo method against various alternatives. The performance of the proposed test with some competing tests is compared. Our results show that our test is superior to the classical nonparametric tests and can apply to a testing problem in practice. A real medical data set is presented and analyzed.


M.E. Ghitany, B. Atieh, and S. Nadarajah Lindley distribution and its Application, Mathematics Computing and Simulation, vol. 78, pp. 493-506, 2008.

R. Shanker, F. Hagos, S. Sujatha On modeling of Lifetimes data using exponential and Lindley distributions, Biometrics &

Biostatistics International Journal, vol. 2, pp. 1-9, 2015.

H. Krishna and K. Kumar Reliability estimation in Lindley distribution with progressively type II right censored sample, Journal of System Assurance Engineering and Management, vol. 82, pp. 281-294, 2011.

P.K. Gupta and B. Singh Parameter estimation of Lindley distribution with hybrid censored data, International Journal of System Assurance Engineering and Management, vol. 4, pp. 378-385, 2013.

D.K. Al-Mutairi, M.E. Ghitany, and D. Kundu Inferences on the stress-strength reliability from Lindley distributions,

Communications in Statistics-Theory and Methods, vol. 42, pp. 1443-1463, 2013.

K. Kumar, H. Krishna, and R. Garg Estimation of P(Y ¡ X) in Lindley distribution using progressively first failure censoring,

International Journal of System Assurance Engineering and Management, vol. 6, pp. 330-341, 2015.

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, vol. 5, pp. 53-96, 2015.

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, vol. 1, pp. 1-34, 2016.

J. Mazucheli, E.A. Coelho-Barros, and F. Louzada On the hypothesis testing for the weighted Lindley distribution, Chilean Journal of Statistics, vol. 7, pp. 17-27, 2016.

M. Ibrahim, A.S. Yadav, H.M. Yousof, H. Goual, and G.G. Hamedani A new extension of Lindley distribution: modified validation test, characterizations and different methods of estimation, Communications for Statistical Applications and Methods, vol. 26, pp. 473-495, 2019.

M.C. Pardo A test for uniformity based on informational energy, Statistical Papers, vol. 44, pp. 521-534, 2003.

H. Alizadeh Noughabi and M. Chahkandi Informational energy and its application in testing normality, Annals of Data Science, vol. 2, pp. 391-401, 2015.

H. Alizadeh Noughabi and J. Jarrahiferiz Informational energy-based goodness-of-fit test for Laplace distribution, International Journal of Information and Decision Sciences, vol. 11, pp. 256-267, 2019.

H. Alizadeh Noughabi, H. Alizadeh Noughabi, and J. Jarrahiferiz Informational Energy and Entropy Applied to Testing

Exponentiality, Statistics, Optimization & Information Computing, vol. 8, pp. 220-228, 2020.

H. Alizadeh Noughabi Testing the Validity of Cauchy Model Based on the Informational Energy, International Journal of Information and Decision Sciences, In Press, 2021.

R.B. DAgostino and M.A. Stephens (Eds.) Goodness-of-fit Techniques, New York: Marcel Dekker, 1986.

B.S. Dhillon Lifetime Distributions, IEEE Transactions on Reliability, vol. 30, pp. 457-459, 1981.

Z. Chen A new two-parameter lifetime distribution with bathtub shape or increasing failure note function, Statistics and Probability Letters, vol. 49, pp. 155-161, 2000.

A. Bekker, J. Roux, and P. Mostert A generalization of the compound Rayleigh distribution: using a Bayesian methods on cancer survival times, Communications in Statistics-Theory and Methods, vol. 29, pp. 1419-1433, 2000.

D.M. Stablein, W.H. Carter, and J.W. Novak Analysis of survival data with nonproportional hazard functions, Controlled Clinical Trials, vol. 2, pp. 149-159, 1981.

M.M. Badr Goodness-of-fit tests for the Compound Rayleigh distribution with application to real data, Heliyon, vol. 5, e02225, 2019.

How to Cite
Alizadeh Noughabi, H. (2021). Testing the Validity of Lindley Model Based on Informational Energy with Application to Real Medical Data. Statistics, Optimization & Information Computing, 10(2), 372-382. https://doi.org/10.19139/soic-2310-5070-1238
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