On Zero-Truncation of Poisson, Poisson-Lindley and Poisson-Sujatha Distributions and their Applications

Detailed study of Lindley distribution (1.3) has been done by Ghitany et al. [4] and shown that (1.3) is a better model than exponential distribution for modeling some lifetime data. Recently, Shanker et al. [5] showed that (1.3) is not always a better model than the exponential distribution for modeling lifetime’s data. In fact, Shanker et al. [5] has done a very extensive and comparative study on modeling of lifetime data using exponential and Lindley distributions and discussed various lifetime data-sets to show the superiority of Lindley over exponential and that of exponential over Lindley distribution. The PLD has been extensively studied by Sankaran [1] and Ghitany & Mutairi [6] and its various properties have been discussed by them. The Lindley distribution and the PLD have been generalized by many researchers. Shanker & Mishra [7] obtained a two parameter Poisson-Lindley distribution by compounding Poisson distribution with a two parameter Lindley distribution introduced by Shanker & Mishra [8]. A quasi Poisson-Lindley distribution has been introduced by Shanker & Mishra [9] by compounding Poisson distribution with a quasi Lindley distribution introduced by Shanker & Mishra [10]. Shanker et al. [11] obtained a discrete two parameter PoissonLindley distribution by mixing Poisson distribution with a two parameter Lindley distribution for modeling waiting and survival times data introduced by Shanker et al. [12]. Further, Shanker & Tekie [13] obtained a new quasi Poisson-Lindley distribution by compounding Poisson distribution with a new quasi Lindley distribution introduced by Shanker & Amanuel [14]. Volume 3 Issue 5 2016