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Abstract:
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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 roots of the quadratic equation turn out to be complex and hence the method fails. In this paper, a methodology based on a quadrature formula of numerical integration is proposed for estimation of the moments. The peak and tail characteristics of a distribution are explained by the standardized fourth central moment, i.e., the coefficient of kurtosis. To incorporate information about these characteristics, a methodology based on the first four sample moments is also proposed here. These methods have been applied to a data set consisting of the duration of hospital stay of geriatric patients. We have also applied the proposed methodology to estimate parameters of an extremely useful model used in pharmacokinetic analysis and illustrated this using a drug concentration data set. It has been shown that methods using all four moments perform better than those based on only the first three moments.
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