Estimation of Morisita Overlapping Measure λ for Two Weibull Distributions

The Morisita's measure <i>λ</i> is an overlapping coefficient between two probability density functions. It is defined as the similarity or agreement between two distributions. The parametric method to estimate this coefficient assumes that the underlying distributions for the two samples at hand are known with unknown parameters. Weibull distribution is one of the important statistical distributions because it is flexible distribution and it is used by scientist in different area of sciences. In this paper, new estimators for the Morisita measure λ are proposed under the parametric Weibull distributions. The derivation of the proposed estimators is based on a new technique that relies entirely on writing the formula of <i>λ</i> as expectation for some functions and then estimating the resulting expectation instead of estimating the exact integral of the formula of <i>λ</i>. In contrast to most studies in the literature, which assumed that the shape parameters of Weibulll distributions are equal, this paper proposes a new technique that enables us to derive new estimators for <i>λ</i> without putting any assumptions about the parameters of Weibull distributions. The performance of the resulting estimators are investigated and compared with the nonparametric kernel estimator and some existing estimators by performing an extensive simulation study. The numerical results showed that the performances of the proposed estimators are better than that of the kernel estimator for almost all considered cases.