Information Theoretic Estimation Improvement to the Nonlinear Gompertz�s Model Based on Ranked Set Sampling

Keywords

Generalized Maximum Entropy, Ranked Set Sampling, Gompertz�s Model Maximum Likelihood Estimates, Monte Carlo experiments

Abstract

The aim of this paper is to apply both Generalized Maximum Entropy (GME) estimation method and Ranked Set Sampling (RSS) technique to improve the estimations of the Gompertz�s Model. The Gompertz�s model is a simple formula which expresses the geometrical relationship between the force of mortality and age. The choice of evaluating the RSS is due to the fact that in many practical applications of the Gompertz�s model, as in biological or environmental sciences, the variable of interest is more costly to measure but is associated with several other easily obtainable. In this paper, we have used Monte Carlo experiments to illustrate the performance of the GME estimator based on two different sampling techniques: the Simple Random Sample (SRS) and RSS. Moreover, the results are compared with the traditional Maximum Likelihood Estimates (MLE).

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