Statistical Properties and Estimation of the Three-Parameter Lindley Distribution with Application to COVID-19 Data

Abstract

In a recent article by Shanker et al. (2017), the three-parameter Lindley distribution has been studied. The present paper is a continuation of the investigation of the properties of this distribution because of its high flexibility for modeling lifetime data. We studied some statistical properties of this distribution as central tendency measures, dispersion measures, and shape measures. In addition, the mode and the quantile function of the distribution were derived by the authors. The three parameters were estimated by the Maximum Product of Spacing Method (MPS) due to its fame in estimating parameters. A simulation study is carried out to examine the consistency of estimators using mean square error (MSE). The estimators showed that they have the property of consistency because MSEs decrease with increasing the size of the sample. On the practical side, the MPS estimates were used to obtain statistical properties, probability density function (p.d.f), cumulative distribution function (c.d.f), survival function, and hazard function for real data which represents COVID-19 Data in Iraq/Al-Anbar Province. We found the flexibility of the distribution in representing life data and the possibility of getting the patients' probability of death and probability of survival for the time.