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Most studies of estimating overlapping coefficients assume two specific parametric models for population densities. The methods that used such of this assumption are called parametric methods, which work well when these model assumptions are valid. Violation of parametric model assumption often leads to a poor estimation. The alternative nonparametric methods are more flexible than the parametric one and they required no assumptions about the parametric structure of population densities. Recently, some efforts were introduced to estimate the overlapping coefficients non-parametrically. In this paper, we introduced the nonparametric kernel method to estimate the three overlapping coefficients that known in the literature as Matusita's measure ρ , Morisita's measure λ and Weitzman's measure Δ. As the simulation results shown and based on the relative root mean square error (RRMSE) measure, if the two population distributions are assumed to be known then the parametric method performs better than the nonparametric kernel method. If there is no information about the structural form of the population distributions then the performance of the kernel method is very acceptable and it performs better than the parametric one. [ABSTRACT FROM AUTHOR]

This paper deals with a new simple one-term approximation to the cumulative distribution function (cdf) of the standard normal distribution which does not have a closed-form representation. The accuracy of the proposed approximation has been evaluated by using the maximum absolute error (MAE), which was about 0.0016 and this accuracy is sufficient for most practical applications. To compare the proposed approximation with some of the existing one-term approximations, the MAE measure was considered. In addition, the difference between the exact and approximation of the normal cdf was computed for specific values of the normal random variable. [ABSTRACT FROM AUTHOR]

The non-parametric kernel density estimation is used in practice to estimate population abundance using the line transect sampling method. Kernel estimator of f(0) usually produces an underestimated value. Assuming the kernel method, this article applies shifted logarithmic transformation to line transect data that violating shoulder condition. Mathematically, the proposed log-transform estimator was shown to be more efficient than the classical kernel estimator. The simulation results present the good properties of the proposed estimator compared to the performance of the classical kernel estimators. [ABSTRACT FROM AUTHOR]

This article proposes nine new approximations for the standard normal cumulative distribution function Φ z. In addition, it collects most of the approximations existing in the literature. The accuracy of the proposed approximations is evaluated by using the maximum absolute error and the mean absolute error. The maximum absolute errors fall between 0.0422613 × 10−6 and 950.55 × 10−6, which indicates high accuracy for some of them. A comparison study between the different existing approximations and the proposed approximations is also accomplished. [ABSTRACT FROM AUTHOR]

We investigate some possibilities for improvements of kernel density estimates using line transect sampling. A bias correction approach is used which produces a new estimator for density of object D . The asymptotic bias of kernel estimator is subtracted from the kernel estimator to form the proposed estimator. It reduced the bias from O ( h 2 ) to O ( h 3 ) as h ? 0 under the shoulder condition assumption and in some cases the bias reduced to O ( h 4 ). The asymptotic theoretical properties of the proposed estimator are presented and the optimal formula for the bandwidth parameter h is given based on minimizing the asymptotic mean square error (AMSE). Moreover, in the absence of our knowledge whether or not the shoulder condition is valid another estimator is suggested, small-sample properties of the proposed estimators are studied and compared with some existing estimators by simulation technique. The results show the superiority of the proposed estimators among the other estimators for most cases considered. [ABSTRACT FROM AUTHOR]