Applications of Mathematical Sciences

Empirical Performance of Nonparametric Kernel Estimators with Data-Driven Bandwidths for Lifetime Distributions

2023-10-12T07:18:38+00:00

During the past several years, many methods for selecting the smoothing parameter have been added in the field of nonparametric kernel regression. The performance of newly introduced selection methods differs quite a little bit, but it is better to consider the recently developed methods for the comparison. Due to the demand for automatic data driven bandwidth selectors for practical statistics, specifically with lifetime distributions, this article provides a review to explain and compare these methods. We conducted an extensive simulation study along with varied estimators and sample sizes to assess the relative performance of the 20 selection methods. From MSEs of simulation, the suitable selection criteria are provided for a suitable bandwidth selection for both classical and plug-in categories. Also, we illustrated these methods with a real example, where we concluded that GCV and Mallow’s Cp perform better with LOWESS estimator.

Time Series Analysis and Forecasting on Import of Palm Oil in Pakistan

2023-10-12T07:27:17+00:00

Pakistan is an agricultural land but due to some substances, Pakistan does not produce Palm oil in the large quantities; therefore, we import palm oil from other countries. For country planning, forecasting is the primary tool for predicting the import of palm oil to determine the situation and what would be the value of import in the coming year. In this research, we applied various time series models and the best model is identified for the objective to forecast the import of palm oil in Pakistan. It is found that the best model is ARIMA (1, 0, 1). Based on this selected model, forecasting the import of palm oil in Pakistan using the Box-Jenkins modelling technique is helpful for better planning and improvement of this agriculture sector of Pakistan.

Linearization Of Nonlinear Sixth-Order Differential Equation By Generalized Sundman Transformation

2024-04-22T07:48:03+00:00

In this study, we present the linearization problem of sixth-order ordinary differential equation under the generalized Sundman transformation X=F(t,x) dt=G(t,x)dt. We found the necessary and sufficient conditions which allow the sixth-order ordinary differential equation, x^6 to be transformed to X^6(T)=0. The process of getting the linearizing transformation is constructed proportionally and explicitly. Some examples of linearizable equation are provided to demonstrate our procedure.

Investigation of MHD Non-Newtonian Fluid in an Inclined Tube with Cilia Effects and Condition at the Convective Boundary

2024-05-15T07:57:18+00:00

This paper deals with the exploration of MHD Jeffrey six constant fluid with effects and convective boundary condition in an inclined tube. Mixed convection circumstances' significance is also explored. Using the assumptions of low Reynolds number and long
wave length, the governing equations of non-Newtonian fluid and heat are first simulated and then condensed. The homotopy perturbation approach (HPM) is implemented to solve the velocity profile for velocity when determining the accurate solutions for the
temperature equation. With the use of graphs, the established formulas for the profile of temperature and velocity are illustrated, and the consequences of different newly emerging parameters are explored for modified peristaltic waves. It has been established that the heat transfer decreases as the Biot number will increase.