Abstract:The purpose of this study is to present a generalized class of estimators using the three-stage Optional Randomized Response Technique (ORRT) in the presence of non-response and measurement errors on a sensitive study variable. The proposed estimator makes use of dual auxiliary information. The expression for the bias and mean square error of the proposed estimator are derived using Taylor series expansion. The proposed estimator’s applicability is proven using real data sets. A numerical study is used to compare the efficiency of the proposed estimator with adapted estimators of the finite population mean. The suggested estimator performs better than adapted ordinary, ratio, and exponential ratio-type estimators in the presence of both non-response and measurement errors. The efficiency of the proposed estimator of population mean declines as the inverse sampling rate, non-response rate, and sensitivity level of the survey question increase.

Abstract:Second-order macroscopic vehicular traffic flow models are categorized under two broad headings based on the direction of their characteristics. Faster-than-vehicle waves are often called isotropic models vis-\'{a}-vis anisotropic models with slower-than-vehicle characteristic speed. The dispute on the supremacy among these families of models is the motivation for this paper. This paper compares and contrasts six distinctive second-order macroscopic models using a numerical simulation and analysis. Three models are characterized by faster-than-vehicle waves with their corresponding anisotropic counterparts. Simulation results on the formation of deceleration waves and the dissolution of acceleration fans are presented to graphically compare the wave profiles of the selected isotropic and anisotropic traffic models. Observably, these opposing models can all characterize these physical traffic phenomena to the same degree. Thus, faster characteristic speed conceptualization of second-order macroscopic equations does not tantamount to model failure but rather lies in the explanation of this property.

Abstract:In this paper, the comparative study of Fadugba-Falodun Scheme (FFS) and the Improved Euler’s Method (IEM) is presented. IEM and FFS have been used successfully for the solution of second order ordinary differential equation. FFS is a numerical method recently proposed by means of an interpolating function involving a transcendental function of exponential type. In order to discuss the efficiency and accuracy of the two methods, an illustrative example has been presented in the context of the Exact Solution (ES) and the absolute relative errors computed at each mesh point of the integration interval under consideration. The numerical results show that there is no significant difference between the FFS and ES, unlike its counterpart IEM. Hence, FFS is a good numerical method for the solution of the second order initial value problem in ordinary differential equations. All calculations have been carried out via MATLAB (R2014a) in double precision.