Size Biased Lindley Distribution and Its Properties a Special Case of Weighted Distribution

Download Download as PDF (Size:4699KB)  HTML   XML  PP. 808-819  
DOI: 10.4236/am.2017.86063    242 Downloads   328 Views  
Author(s)    Leave a comment


The purpose of this paper is to introduce a size biased Lindley distribution which is a special case of weighted distributions. Weighted distributions have practical significance where some types of biased occur in a density function, i.e. probability is proportional to the size of the variate, that’s why the proposed version of size biased Lindley is designed for such situations more reasonably and more precisely. Principle properties of the density function are also discussed in this paper such as moments, measure of skewness, kurtosis, moment generating function, characteristics generating function, coefficient of variation, survival function and hazard function which are derived for understanding the structure of the proposed distribution more briefly.

Cite this paper

Ayesha, A. (2017) Size Biased Lindley Distribution and Its Properties a Special Case of Weighted Distribution. Applied Mathematics, 8, 808-819. doi: 10.4236/am.2017.86063.


[1] Bhati, D., Malik, M.A. and Vaman, H.J. (2014) Lindley-Exponential Distribution: Properties and Applications. Metron, 73, 335-357.
[2] Borah, M. and Nathl, A.D. (2001) A Study on the Inflated Poisson Lindley Distribution. Journal of the Indian Society of Agricultural Statistics, 54, 317-323.
[3] Das, K.K. and Roy, T.D. (2011) Applicability of Length Biased Weighted Generalized Rayleigh Distribution. Advances in Applied Science Research, 2, 320-327.
[4] Elbatal, I., Merovci, F. and Elgarhy, M. (2013) A New Generalized Lindley Distribution. Mathematical Theory and Modeling, 3, 30-47.
[5] Ghitany, M.E. and Al-Mutairi, D.K. (2008) Size-Biased Poisson-Lindley Distribution and Its Application. Metron-International Journal of Statistics, 66, 299-311.
[6] Ghitany, M.E., Atieh, B. and Nadarajah, S. (2008) Lindley Distribution and Its Application. Mathematics and Computers in Simulation, 78, 493-506.
[7] Ghitany, M.E., Al-Mutairi, D.K. and Nadarajah, S. (2008) Zero-Truncated Poisson-Lindley Distribution and Its Application. Mathematics and Computers in Simulation, 79, 279-287.
[8] Ghitany, M.E., Alqallaf, F., Al-Mutairi, D.K. and Husain, H.A. (2011) A Two-Parameter Weighted Lindley Distribution and Its Applications to Survival Data. Mathematics and Computers in Simulation, 81, 1190-1201.
[9] Lord, D. and Geedipally, S.R. (2011) The Negative Binomial-Lindley Distribution as a Tool for Analyzing Crash Data Characterized by a Large Amount Of Zeros. Accident Analysis & Prevention, 43, 1738-1742.
[10] Mazucheli, J. and Achcar, J.A. (2011) The Lindley Distribution Applied to Competing Risks Lifetime Data. Computer Methods and Programs in Biomedicine, 104, 188-192.
[11] Merovci, F. and Sharma, V.K. (2014) The Beta-Lindley Distribution: Properties and Applications. Journal of Applied Mathematics, 2014, Article ID: 198951.
[12] Mir, K.A. and Ahmad, M. (2009) Size-Biased Distributions and Their Applications. Pakistan Journal of Statistics, 25, 283-294.
[13] Patil, G.P. and Rao, C.R. (1978) Weighted Distributions and Size-Biased Sampling with Applications to Wildlife Populations and Human Families. Biometrics, 34, 179-189.
[14] Ratnaparkhi, M.V. and Naik-Nimbalkar, U.V. (2012) The Length-Biased Lognormal Distribution and Its Application in the Analysis of Data from Oil Field Exploration Studies. Journal of Modern Applied Statistical Methods, 11, 22.
[15] Shanker, R., Sharma, S. and Shanker, R. (2013) A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data. Applied Mathematics, 4, 363-368.
[16] Singh, S.K., Singh, U. and Sharma, V.K. (2014) The Truncated Lindley Distribution: Inference and Application. Journal of Statistics Applications & Probability, 3, 219-228.
[17] Wang, M. (2013) A New Three-Parameter Lifetime Distribution and Associated Inference. arXiv:1308.4128
[18] Zakerzadeh, H. and Dolati, A. (2009) Generalized Lindley Distribution. Journal of Mathematical Extension, 3, 13-25.

comments powered by Disqus

Copyright © 2017 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.