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In this article, we have considered one parameter polynomial exponential(OPPE) distribution. The exponential, Lindley, length-biased Lindley andSujatha distribution are particular cases. Two estimators viz, MLE and UMVUE ofthe PDF and the CDF of the OPPE distribution have been discussed. Theestimation issue of the length-biased Lindley and Sujatha distribution havebeen considered in detail. The estimators have been compared in MSE sense.Monte Carlo simulations and real data analysis are performed to compare theperformances of the proposed methods of estimation.

Study on estimators of the PDF and CDF of the one parameter polynomial exponential distribution