A Two-Parameter Lindley Distribution

• Authors: Shanker R. , Mishra A.
• Languages of publication: EN

Abstracts

EN

A two-parameter Lindley distribution, of which the Lindley distribution (LD) is a particular case, has been introduced. Its moments, failure rate function, mean residual life function and stochastic orderings have been discussed. The maximum likelihood method and the method of moments have been discussed for estimating its parameters. The distribution has been fitted to some data-sets to test its goodness of fit.

Keywords

EN

Lindley distribution; moments; failure rate function; mean residual life function; stochastic ordering; estimation of parameters; goodness of fit

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2013
• Volume: 14
• Issue: 1
• Pages: 45-56

Contributors

author

Shanker R.

• College of Business and Economics

author

Mishra A.

• Patna University

References

• BAKOUCH, H. S., AL-ZAHRANI, B. M., AL-SHOMRANI, A. A., MARCHI, V. A. A., LOUZADA, F., (2012). An extended Lindley distribution, Journal of the Korean Statistical Society, Vol. 41 (1), 75-85.
• BJERKEDAL, T., (1960). Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli, American Journal of Epidemiol, Vol. 72 (1), 130-148.
• DENIZ, E. G., and OJEDA, E. C., (2011). The discrete Lindley distribution-Properties and Applications, Journal of Statistical Computation and Simulation, Vol. 81 (11), 1405-1416.
• GHITANY, M. E., ATIEH, B., NADARAJAH, S., (2008). Lindley distribution and its Applications, Mathematics and Computers in Simulation, Vol. 78(4), 493-506.
• GHITANY, M. E., AL-MUTAIRI, D. K., NADARAJAH, S., (2008). Zero-truncated Poisson-Lindley distribution and its Applications, Mathematics and Computers in Simulation, Vol. 79(3), 279-287.
• GHITANY, M. E. and AL-MUTAIRI, D. K., (2008). Size-biased Poisson-Lindley distribution and its Applications, Metron-International Journal of Statistics, Vol. LXVI, no. 3, 299-311.
• GHITANY, M. E. and AL-MUTAIRI, D. K., (2009). Estimation methods for the discrete Poisson- Lindley distribution, Journal of Statistical Computation and Simulation, Vol. 79 (1), 1-9.
• GHITANY, M. E. AL-QALLAF, F., AL-MUTAIRI, D. K., HUSSAIN, H. A., (2011). A two parameter weighted Lindley distribution and its applications to survival data, Mathematics and Computers in Simulation, Vol. 81 (6), 1190- 1201.
• LINDLEY, D. V., (1958). Fiducial distributions and Bayes’ theorem, Journal of the Royal Statistical Society, Series B, 20, 102-107.
• LINDLEY, D. V., (1965). Introduction to Probability and Statistics from Bayesian viewpoint, part II, Inference, Cambridge university press, New York.
• MAHMOUDI, E. and ZAKERZADAH, H., (2010). Generalized Poisson Lindley distribution, Communications in Statistics-Theory and Methods, 39, 1785-1798.
• MAZUCHELI, J. and ACHCAR, J. A., (2011). The Lindley distribution applied to competing risks lifetime data, Computer Methods and Programs in Biomedicine, Vol. 104 (2), 188-192.
• PARANJPE, S. and RAJARSHI, M. B., (1986). Modeling non-monotonic survivorship data with bath tube distributions, Ecology, Vol. 67 (6), 1693-1695.
• SANKARAN, M., (1970). The discrete Poisson-Lindley distribution, Biometrics, 26, 145-149.
• SHAKED, M. and SHANTHIKUMAR, J. G., (1994). Stochastic Orders and Their Applications, Academic Press, New York.
• ZAKERZADAH, H. and DOLATI, A., (2009). Generalized Lindley distribution, Journal of Mathematical Extension, Vol. 3(2), 13-25.
• ZAMANI, H. and ISMAIL, N., (2010). Negative Binomial- Lindley distribution and its Applications, Journal of Mathematics and Statistics, Vol. 6(1), 4-9.