in this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by jones [12] for length-biased data.the approach is based on the invariance principle for the empirical processes proved by horváth [10]. all simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...

the purpose of this paper is to provide some asymptotic results for nonparametric estimator of the lorenz curve and lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. first, we show that nonparametric estimator of the lorenz curve is uniformly strongly consistent for the associated lorenz curve. also, a strong gaussian approximation for ...

We establish the optimal rates of strong approximation by Wiener process for vector-valued cumulative processes. The Komlós–Major–Tusnády bounds are given both in case when exponential moments exist and power case. Applications to invariance principle stopped sums birth death processes provided. As a tool we use maximal inequality over random intervals which is independent interest.

The purpose of this paper is to provide some asymptotic results for nonparametric estimator of the Lorenz curve and Lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. First, we show that nonparametric estimator of the Lorenz curve is uniformly strongly consistent for the associated Lorenz curve. Also, a strong Gaussian approximation for ...

In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...

In recent years, there has been considerable interest in the use of CDMA in mobile communications. Bit error rate is one of the most important parameters in the evaluation of CDMA systems. In this paper, we develop a technique to find an accurate approximation to the probability of bit error for asynchronous direct–sequence code division multiple–access (DS/CDMA) systems by modeling the multipl...

in this paper, a class of semi-implicit two-stage stochastic runge-kutta methods (srks) of strong global order one, with minimum principal error constants are given. these methods are applied to solve itô stochastic differential equations (sdes) with a wiener process. the efficiency of this method with respect to explicit two-stage itô runge-kutta methods (irks), it method, milstien method, sem...