View Submission - COMPSTAT2022

A0432
**Title: **Estimation of parameters of a mixture of two exponential distributions
**Authors: **Trijya Singh - Le Moyne College, Syracuse, NY (United States) **[presenting]**

**Abstract: **For estimating the parameters of a mixture of two exponential distributions, the method of moments, which uses roots of a quadratic equation involving the estimates of the first three raw moments has been used in the past. Because of poor estimates of these moments, in many situations, the roots of the quadratic equation turn out to be complex and hence the method fails. A methodology based on a quadrature formula of numerical integration is proposed for the estimation of the moments. These moment estimates always produce real roots of the quadratic equation in the case of sampling from a mixture of two exponential distributions and produce estimates of the parameters. To fully capture the long tail or heavy tail behavior of mixture models, the peak and tail characteristics of a distribution that are explained by the standardized fourth central moment (the coefficient of kurtosis) are incorporated into the proposed methodology by using the first four sample moments. The estimates obtained by the method of moments are proposed as initial estimates for an optimization algorithm to obtain least squares estimates. Some important applications have been discussed using a drug concentration dataset, and it has been shown that methods using all four moments perform better than those based on only the first three moments.