A New Generalized Poisson-Lindley Distribution: Applications and Properties
A new generalized Poisson Lindley distribution is obtained by compounding Poisson
distribution with two parameter generalised Lindley distribution. The new distribution is
shown to be unimodal and over dispersed. This distribution has a tendency to accommodate right tail as well as for particular values of parameter the tail tends to zero at a faster rate. Various properties like cumulative distribution function, generating function, Moments etc. are derived. Knowledge about the parameters is obtained through Method of Moments, Maximum Likelihood Method and EM Algorithm. Moreover, an actuarial application in collective risk model is shown by considering the proposed distribution as primary and Exponential and Erlang as secondary distribution. The model is applied to real dataset and found to perform better than competing models.
Chakraborty S.(2010): On Some Distributional Properties of the Family of Weighted Generalized Poisson Distribution, Communications in Statistics - Theory and Methods, Vol(39:15), 2767-2788.
Dempster, A.P., Laird, N.M. and Rubin, D. (1977): Maximum Likelihood form Incomplete Data Via th M Algorithm. Journal of th Royal Statistical Society, B 39, 1-38.
Ghitany M.E., Atieh B. and Nadarajah S.(2008) Lindley distribution and its application, Mathematics and Computers in Simulation, Vol(78), 493-506.
Ghitany M.E., Atieh B. and Nadarajah S.(2008) Zero-truncated Poisson Lindley distribution and its application, Mathematics and Computers in Simulation, 79, 279-287.
Gomez D.E. and Ojeda E.C.(2011): The discrete Lindley distribution:properties and applications, Journal of Statistical Computation and Simulation, Vol(81:11), 1405-1416.
Gomez D.E. and Ojeda E.C.(2013): The Compound DGL/Erlang Distribution in the Collective Risk Model, Journal of Quantitative Methods for Economics and Business Administration, Vol(16), 121-142.
Johnson, N.L., Kemp, A.W., Kotz, S.(2005): Univariate Discrete Distributions. Wiley, New York.
Jorda P.,(2010): Computer generation of random variables with Lindley or Poisson-Lindley distribution via the Lambert W function, Mathematics and Computers in Simulation, Vol(81), 851-859.
Karlis D., (2005) EM Algorithm for mixed poisson and other discrete distributions, Astin Bulletin, Vol(35:1), 3-24.
Lindley D. V.,(1958) Fiducial distributions and Bayes theorem, Journal of the Royal Statistical Society, Series B (Methodological),102-107.
Mahmoudi E. and Zakerzadeh H.(2010): Generalized PoissonLindley Distribution, Communications in Statistics - Theory and Methods, Vol(39:10), 1785-1798.
Sankaran M.(1970): The Discrete Poisson-Lindley Distribution, Biometrics, Vol(26:1), 145-149.
Shanker R., Sharma S. and Shanker R.(2013): A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data, Applied Mathematics, Vol(4), 363-368.
Sundt, B., Vernic, R. (2009). Recursions for Convolutions and Compound Distributions with Insurance Applications. SpringerVerlag, New York.
Zakerzadeh H. and Dolati A.(2009): Generalized Lindley Distribution,Journal of Mathematical Extension, Vol. 3, No. 2, 13-25.
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