Inverted Beta Lindley Distribution
DOI:
https://doi.org/10.24297/jam.v13i1.5857Keywords:
Inverted beta distribution, Lindley distribution, Maximum likelihood estimation, Bladder cancer data, Hazard function, Goodness–of–fit.Abstract
In this paper, a three-parameter continuous distribution, namely, Inverted Beta-Lindley (IBL) distribution is proposed and studied. The new model turns out to be quite flexible for analyzing positive data and has various shapes of density and hazard rate functions. Several statistical properties associated with this distribution are derived. Moreover, point estimation via method of moments and maximum likelihood method are studied and the observed information matrix is derived. An application of the new model to real data shows that it can give consistently a better fit than other important lifetime models.Downloads
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References
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[12] McDonald, J.B., Butler, R.J. (1990). “Regression models for positive random variablesâ€. Journal of Econometrics, 43:227–251.
[13] McDonald, J.B., Richards, D.O. (1987). “Hazard rates and generalized beta distributionâ€. IEEE Transactions on Reliability, 36:463–466.
[14] McDonald, J.B., Richards, D.O. (1987). “Model selection: some generalized distributionsâ€. Communications in Statistics–Theory and Methods, 16:1049–1074.
[15] Merovci, F., Sharma, V.K. (2014). “The Beta-Lindley Distribution: Properties and Applicationsâ€. Journal of Applied Mathematics, 10: 198-951.
[16] Nadarajah, S., Kotz, S. (2006). “The beta exponential distributionâ€. Reliability Engineering and System Safety, 91:689–697.
[17] Nanda, A.K., Singh, H., Misra, N., Paul, P. (2003). “Reliability Properties of Reversed Residual Lifetimeâ€. Communications in Statistics-Theory and Methods, 32(10): 2031-2042.
[18] Pal, M., Tiensuwan, M. (2014). “The Beta Transmuted Weibull Distributionâ€. Austrian Journal of Statistics, 43(2), 133–149.
[19] Vargo, E., Pasupathy, R., Leemis, L. (2010). “Moment-ratio diagrams for univariate distributionsâ€. Journal of Quality Technology, 42:276–286.
[20] Zea, L.M., Silva, R.B, Bourguignon, M., Santos, A.M., Cordeiro, G.M. (2012). “The Beta Exponentiated Pareto Distribution with Application to Bladder Cancer Susceptibilityâ€. International Journal of Statistics and Probability, 2: 1927-7032.
[2] Bookstaber, R.M., McDonald, J.B. (1987). “A general distribution for describing security price returnsâ€. The Journal of Business, 60:401–424.
[3] Cummins, J.D., Dionne, G., McDonald, J.B., Pritchett, B.M. (1990). “Applications of the GB2 family of distributions in modeling insurance loss processesâ€. Insurance: Mathematics and Economics, 9:257–272.
[4] Ghitany, M.E., Atieh, B., Nadarajah, S. (2008). “Lindley Distribution and its Applicationâ€. Mathematics and Computer in Simulation, 78:493–506.
[5] Gupta, P.L., Gupta, R.C. (1983). “On the Moments of Residual life in Reliability and some Characterization Resultsâ€. Communications in Statistics-Theory and Methods, 12(4): 449-461.
[6] Gupta, R. C., Gupta, R. D., Gupta, P. L. (1998). “Modeling failure time data by Lehman alternativesâ€. Communications in Statistics: Theory and Methods, 27:887-904.
[7] Kundu, C., Nanda, A.K. (2010). “Some Reliability Properties of the Inactivity Timeâ€. Communications in Statistics-Theory and Methods, 39: 899-911.
[8] Lee E. T., Wang, J. W. (2003). “Statistical Methods for Survival Data Analysisâ€. John Wiley & Sons, New York, NY, USA, 3rd edition.
[9] Lindley, D. V. (1958). “Fiducial distributions and Bayes' theoremâ€. Journal of the Royal Statistical Society, Series B, 20(1):102–107.
[10] McDonald, J.B., Bookstaber, R.M. (1991). “Option pricing for generalized distributionsâ€. Communications in Statistics–Theory and Methods, 20:4053–4068.
[11] McDonald, J.B., Butler, R.J. (1987). “Some generalized mixture distributions with an application to unemployment durationâ€. The Review of Economics and Statistics, 69:232–240.
[12] McDonald, J.B., Butler, R.J. (1990). “Regression models for positive random variablesâ€. Journal of Econometrics, 43:227–251.
[13] McDonald, J.B., Richards, D.O. (1987). “Hazard rates and generalized beta distributionâ€. IEEE Transactions on Reliability, 36:463–466.
[14] McDonald, J.B., Richards, D.O. (1987). “Model selection: some generalized distributionsâ€. Communications in Statistics–Theory and Methods, 16:1049–1074.
[15] Merovci, F., Sharma, V.K. (2014). “The Beta-Lindley Distribution: Properties and Applicationsâ€. Journal of Applied Mathematics, 10: 198-951.
[16] Nadarajah, S., Kotz, S. (2006). “The beta exponential distributionâ€. Reliability Engineering and System Safety, 91:689–697.
[17] Nanda, A.K., Singh, H., Misra, N., Paul, P. (2003). “Reliability Properties of Reversed Residual Lifetimeâ€. Communications in Statistics-Theory and Methods, 32(10): 2031-2042.
[18] Pal, M., Tiensuwan, M. (2014). “The Beta Transmuted Weibull Distributionâ€. Austrian Journal of Statistics, 43(2), 133–149.
[19] Vargo, E., Pasupathy, R., Leemis, L. (2010). “Moment-ratio diagrams for univariate distributionsâ€. Journal of Quality Technology, 42:276–286.
[20] Zea, L.M., Silva, R.B, Bourguignon, M., Santos, A.M., Cordeiro, G.M. (2012). “The Beta Exponentiated Pareto Distribution with Application to Bladder Cancer Susceptibilityâ€. International Journal of Statistics and Probability, 2: 1927-7032.
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Published
2017-03-30
How to Cite
Kilany, N., & Atallah, H. M. (2017). Inverted Beta Lindley Distribution. JOURNAL OF ADVANCES IN MATHEMATICS, 13(1), 7074–7086. https://doi.org/10.24297/jam.v13i1.5857
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