Abstract
This paper aims to study some properties of the three-parameter Lindley distribution TPLD and the proposed new formula for the TPLD in studying the life-time distribution, survival function, and hazard function. We proposed a new formula for the TPLD by considering the new mixing weights of the mixing function that were used in constructing the TPLD and by replacing the mixing weights in the mixing equation to get a new formula for the TPLD that is called the proposed three-parameter Lindley distribution, and we denoted it by PTPLD. We study some properties of PTPLD in the lifetime distribution. We use three methods of estimation, the method of moments , the MLH method and Standard Bayesian method, to estimate the parameters and the survival functions for the two distributions (TPLD and PTPLD) and compare the survival functions estimates for both distributions using the above three methods of estimation, and we select the best estimate based on some criteria of error. In addition, we used real data from the AL-Hussain Teaching Hospital in Nasiriya City to estimate the survival time of infected patients with COVID-19 using TPLD and PTPLD. It was concluded that the proposed formula for the distribution is the best for all selected sample sizes.
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