The Application of Fractional Calculus in Chinese Economic Growth Models

In this paper, we apply Caputo-type fractional order calculus to simulate China’s gross domestic product (GDP) growth based on R software, which is a free software environment for statistical computing and graphics. Moreover, we compare the results for the fractional model with the integer order model. In addition, we show the importance of variables according to the BIC criterion. The study shows that Caputo fractional order calculus can produce a better model and perform more accurately in predicting the GDP values from 2012–2016.

Download Full-text

LAND-SE: a software for landslide statistically-based susceptibility zonation, Version 1.0

10.5194/gmd-2016-60 ◽

2016 ◽

Cited By ~ 1

Author(s):

Mauro Rossi ◽

Paola Reichenbach

Keyword(s):

Statistical Models ◽

Landslide Susceptibility ◽

Recent Literature ◽

Model Performance ◽

Free Software ◽

Statistical Computing ◽

Software Environment ◽

The World ◽

Analysis Prediction ◽

Mapping Units

Abstract. Landslide susceptibility (LS) provides an estimate of the landslide spatial occurrence based on local terrain conditions. LS has been evaluated in many locations around the world since the early '80 using distinct modelling approaches, diverse combination of variables, and different partition of the territory (mapping units). Among the different methods, statistical models have been largely used to assess LS and several model types have been proposed in the literature. A recent literature review revealed that authors not always present a complete and comprehensive assessment of the LS that includes model performance analysis, prediction skills evaluation and estimation of the errors and uncertainty. The aim of this paper is to describe LAND-SE (LANDslide Susceptibility Evaluation), software that performs susceptibility modelling and zonation using statistical models, quantifies the model performances and the associated uncertainty. The software is implemented in R, a free software environment for statistical computing and graphics. This provides users with the possibility to implement and improve the code with additional models, evaluations tools or output types. The paper describes the software structure, explains input and output, illustrates specific applications with maps and graphs. The LAND-SE script is delivered with a basic user guide and three example datasets.

Download Full-text

Fractional-Order Model Predictive Frequency Control of an Islanded Microgrid

Energies ◽

10.3390/en12010084 ◽

2018 ◽

Vol 12 (1) ◽

pp. 84 ◽

Cited By ~ 14

Author(s):

Min-Rong Chen ◽

Guo-Qiang Zeng ◽

Yu-Xing Dai ◽

Kang-Di Lu ◽

Da-Qiang Bi

Keyword(s):

Cost Function ◽

Fractional Order ◽

Predictive Control ◽

Frequency Control ◽

Optimal Frequency ◽

Order Model ◽

Fractional Order Calculus ◽

Fractional Order Model ◽

Islanded Microgrid ◽

Fractional Order Integral

Optimal frequency control of an islanded microgrid has been a challenging issue in the research field of microgrids. Recently, fractional-order calculus theory and some related control methods have attempted to handle this issue. In this paper, a novel fractional-order model predictive control (FOMPC) method is proposed to achieve the optimal frequency control of an islanded microgrid by introducing a fractional-order integral cost function into model predictive control (MPC) algorithm. Firstly, a discrete state-space model is derived for the optimal frequency control problem of an islanded microgrid. Afterward, a fractional-order integral cost function is designed to guide the FOMPC algorithm to obtain optimal control law by borrowing the Grünwald-Letnikov (GL) definition of fractional order calculus. Six simulation studies have been carried out to illustrate the superiority of FOMPC to conventional MPC under dynamical load disturbances, perturbed system parameters and random dynamical power fluctuation of wind turbines.

Download Full-text

Mortality Statistics and Cause of Death at Duhok City from The Period (2014-2019) Using R Language Data Analytics

Academic Journal of Nawroz University ◽

10.25007/ajnu.v9n3a699 ◽

2020 ◽

Vol 9 (3) ◽

pp. 1

Author(s):

Renas Rajab Asaad ◽

Rezbar F. Mustafa ◽

Shiret I. Hussien

Keyword(s):

Cause Of Death ◽

Death Rate ◽

Data Analytics ◽

Free Software ◽

Statistical Computing ◽

Software Environment ◽

R Language ◽

Language Data ◽

R Programming ◽

Death Causes

Nowadays, the amount of giving birth is increasing by amount of death, these days there are have many death causes (diseases) , in different ways, and there's different death causes in every region, In north of Iraq there is a governorate called Duhok, population of Duhok's governorate is nearly about 1.011.585 people in 2019. Descriptive tabulations of data are presented and interpreted. including rates by cause of death rate, data shown in this article are based on death causes last five years, from Dec of 2014 till the end of 2019 period of analyzing Duhok death’s dataset using R programming, to analyze Age the most death in, disease the most death caused, and month the most death in, by used R. R is a programming language and free software environment for statistical computing and graphics supported by the R Foundation for Statistical Computing.

Download Full-text

LAND-SE: a software for statistically based landslide susceptibility zonation, version 1.0

Geoscientific Model Development ◽

10.5194/gmd-9-3533-2016 ◽

2016 ◽

Vol 9 (10) ◽

pp. 3533-3543 ◽

Cited By ~ 30

Author(s):

Mauro Rossi ◽

Paola Reichenbach

Keyword(s):

Statistical Models ◽

Landslide Susceptibility ◽

Model Performance ◽

Environmental Data ◽

Free Software ◽

Statistical Computing ◽

Data Sets ◽

Software Environment ◽

Analysis Prediction ◽

Mapping Units

Abstract. Landslide susceptibility (LS) assessment provides a relative estimate of landslide spatial occurrence based on local terrain conditions. A literature review revealed that LS evaluation has been performed in many study areas worldwide using different methods, model types, different partition of the territory (mapping units) and a large variety of geo-environmental data. Among the different methods, statistical models have been largely used to evaluate LS, but the minority of articles presents a complete and comprehensive LS assessment that includes model performance analysis, prediction skills evaluation, and estimation of the errors and uncertainty. The aim of this paper is to describe LAND-SE (LANDslide Susceptibility Evaluation) software that performs susceptibility modelling and zonation using statistical models, quantifies the model performances, and the associated uncertainty. The software is implemented in R, a free software environment for statistical computing and graphics. This provides users with the possibility to implement and improve the code with additional models, evaluation tools, or output types. The paper describes the software structure, explains input and output, and illustrates specific applications with maps and graphs. The LAND-SE script is delivered with a basic user guide and three example data sets.

Download Full-text

MAHALANOBIS DISTANCE AND ITS APPLICATION FOR DETECTING MULTIVARIATE OUTLIERS

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi1903583g ◽

2019 ◽

pp. 583

Author(s):

Hamid Ghorbani

Keyword(s):

Mahalanobis Distance ◽

Multivariate Data ◽

Real Data ◽

Statistical Computing ◽

Software Environment ◽

R Software ◽

Multivariate Statistical ◽

Data Set ◽

Multivariate Outliers ◽

Outliers Detection

While methods of detecting outliers is frequently implemented by statisticians when analyzing univariate data, identifying outliers in multivariate data pose challenges that univariate data do not. In this paper, after short reviewing some tools for univariate outliers detection, the Mahalanobis distance, as a famous multivariate statistical distances, and its ability to detect multivariate outliers are discussed. As an application the univariate and multivariate outliers of a real data set has been detected using R software environment for statistical computing.

Download Full-text

Facilitating the analysis of the multifocal electroretinogram using the free software environment R

European Journal of Ophthalmology ◽

10.5301/ejo.5001018 ◽

2018 ◽

Vol 28 (1) ◽

pp. 87-93

Author(s):

Richard Bergholz ◽

Mirjam Rossel ◽

Ralf M. Dutescu ◽

Klaas P. Vöge ◽

Daniel J. Salchow

Keyword(s):

Healthy Subjects ◽

Multifocal Electroretinogram ◽

Free Software ◽

Implicit Time ◽

Control Group ◽

Group Comparison ◽

Bonferroni Correction ◽

Software Environment ◽

R Software ◽

Patient Groups

Purpose: The large amount of data rendered by the multifocal electroretinogram (mfERG) can be analyzed and visualized in various ways. The evaluation and comparison of more than one examination is time-consuming and prone to create errors. Using the free software environment R we developed a solution to average the data of multiple examinations and to allow a comparison of different patient groups. Methods: Data of single mfERG recordings as exported in .csv format from a RETIport 21 system (version 7/03, Roland Consult) or manually compiled .csv files are the basis for the calculations. The R software extracts response densities and implicit times of N1 and P1 for the sum response, each ring eccentricity, and each single hexagon. Averages can be calculated for as many subjects as needed. The mentioned parameters can then be compared to another group of patients or healthy subjects. Application of the software is illustrated by comparing 11 patients with chloroquine maculopathy to a control group of 7 healthy subjects. Results: The software scripts display response density and implicit time 3D plots of each examination as well as of the group averages. Differences of the group averages are presented as 3D and grayscale 2D plots. Both groups are compared using the t-test with Bonferroni correction. The group comparison is furthermore illustrated by the average waveforms and by boxplots of each eccentricity. Conclusions: This software solution on the basis of the programming language R facilitates the clinical and scientific use of the mfERG and aids in interpretation and analysis.

Download Full-text