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Full-Text Articles in Computer Engineering

Relating Admissibility Standards For Digital Evidence To Attack Scenario Reconstruction, Changwei Liu, Anoop Singhal, Duminda Wijesekera Jan 2014

Relating Admissibility Standards For Digital Evidence To Attack Scenario Reconstruction, Changwei Liu, Anoop Singhal, Duminda Wijesekera

Journal of Digital Forensics, Security and Law

Attackers tend to use complex techniques such as combining multi-step, multi-stage attack with anti-forensic tools to make it difficult to find incriminating evidence and reconstruct attack scenarios that can stand up to the expected level of evidence admissibility in a court of law. As a solution, we propose to integrate the legal aspects of evidence correlation into a Prolog based reasoner to address the admissibility requirements by creating most probable attack scenarios that satisfy admissibility standards for substantiating evidence. Using a prototype implementation, we show how evidence extracted by using forensic tools can be integrated with legal reasoning to reconstruct …


Audit: Automated Disk Investigation Toolkit, Umit Karabiyik, Sudhir Aggarwal Jan 2014

Audit: Automated Disk Investigation Toolkit, Umit Karabiyik, Sudhir Aggarwal

Journal of Digital Forensics, Security and Law

Software tools designed for disk analysis play a critical role today in forensics investigations. However, these digital forensics tools are often difficult to use, usually task specific, and generally require professionally trained users with IT backgrounds. The relevant tools are also often open source requiring additional technical knowledge and proper configuration. This makes it difficult for investigators without some computer science background to easily conduct the needed disk analysis. In this paper, we present AUDIT, a novel automated disk investigation toolkit that supports investigations conducted by non-expert (in IT and disk technology) and expert investigators. Our proof of concept design …


Evidentiary Power And Propriety Of Digital Identifiers And The Impact On Privacy Rights In The United States, Michael Losavio, Deborah Keeling Jan 2014

Evidentiary Power And Propriety Of Digital Identifiers And The Impact On Privacy Rights In The United States, Michael Losavio, Deborah Keeling

Journal of Digital Forensics, Security and Law

Media and network systems capture and store data about electronic activity in new, sometimes unprecedented ways; computational systems make for new means of analysis and knowledge development. These new forms offer new, powerful tactical tools for investigations of electronic malfeasance under traditional legal regulation of state power, particular that of Fourth Amendment limitations on police searches and seizures under the U.S. Constitution. But autonomy, identity and authenticity concerns with electronic data raise issues of public policy, privacy and proper police oversight of civil society. We examine those issues and their implications for digital and computational forensics


Effects Of The Factory Reset On Mobile Devices, Riqui Schwamm, Neil C. Rowe Jan 2014

Effects Of The Factory Reset On Mobile Devices, Riqui Schwamm, Neil C. Rowe

Journal of Digital Forensics, Security and Law

Mobile devices usually provide a “factory-reset” tool to erase user-specific data from the main secondary storage. 9 Apple iPhones, 10 Android devices, and 2 BlackBerry devices were tested in the first systematic evaluation of the effectiveness of factory resets. Tests used the Cellebrite UME-36 Pro with the UFED Physical Analyzer, the Bulk Extractor open-source tool, and our own programs for extracting metadata, classifying file paths, and comparing them between images. Two phones were subjected to more detailed analysis. Results showed that many kinds of data were removed by the resets, but much user-specific configuration data was left. Android devices did …


Testing Framework For Mobile Device Forensics Tools, Maxwell Anobah, Shahzad Saleem, Oliver Popov Jan 2014

Testing Framework For Mobile Device Forensics Tools, Maxwell Anobah, Shahzad Saleem, Oliver Popov

Journal of Digital Forensics, Security and Law

The proliferation of mobile communication and computing devices, in particular smart mobile phones, is almost paralleled with the increasing number of mobile device forensics tools in the market. Each mobile forensics tool vendor, on one hand claims to have a tool that is best in terms of performance, while on the other hand each tool vendor seems to be using different standards for testing their tools and thereby defining what support means differently. To overcome this problem, a testing framework based on a series of tests ranging from basic forensics tasks such as file system reconstruction up to more complex …


Technical Soddi Defenses: The Trojan Horse Defense Revisited, Chad M. Steel Jan 2014

Technical Soddi Defenses: The Trojan Horse Defense Revisited, Chad M. Steel

Journal of Digital Forensics, Security and Law

In 2004, the Trojan horse defense was at a crossroads, having been successfully employed in two child pornography cases in the United Kingdom, resulting in acquittals. Despite the early successes, the Trojan horse defense has failed to become a regularly employed strategy. The original Trojan horse defense has now become part of the more general technical SODDI (Some Other Dude Did It) defense, which includes the possibility of unknown actors using unsecured Wi-Fi connections or having physical access to a computer to perform criminal acts. In the past ten years, it has not been effective in the United States for …


Table Of Contents Jan 2014

Table Of Contents

Journal of Digital Forensics, Security and Law

No abstract provided.


A State-Of-The-Art Review Of Cloud Forensics, Sameera Almulla, Youssef Iraqi, Andrew Jones Jan 2014

A State-Of-The-Art Review Of Cloud Forensics, Sameera Almulla, Youssef Iraqi, Andrew Jones

Journal of Digital Forensics, Security and Law

Cloud computing and digital forensics are emerging fields of technology. Unlike traditional digital forensics where the target environment can be almost completely isolated, acquired and can be under the investigators control; in cloud environments, the distribution of computation and storage poses unique and complex challenges to the investigators. Recently, the term “cloud forensics” has an increasing presence in the field of digital forensics. In this state-of-the-art review, we included the most recent research efforts that used “cloud forensics” as a keyword and then classify the literature into three dimensions: (1) survey-based, (2) technology-based and (3) forensics-procedural-based. We discuss widely accepted …


Understanding Computer Forensics Requirements In China Via The “Panda Burning Incense” Virus Case, Frank Law, K. P. Chow, Y. H. Mai Jan 2014

Understanding Computer Forensics Requirements In China Via The “Panda Burning Incense” Virus Case, Frank Law, K. P. Chow, Y. H. Mai

Journal of Digital Forensics, Security and Law

In March 2012, Mainland China has amended its Criminal Procedure Law, which includes the introduction of a new type of evidence, i.e., digital evidence, to the court of law. To better understand the development of computer forensics and digital evidence in Mainland China, this paper discusses the Chinese legal system in relation to digital investigation and how the current legal requirements affect the existing legal and technical usage of digital evidence at legal proceedings. Through studying the famous “Panda Burning Incense (Worm.WhBoy.cw)” virus case that happened in 2007, this paper aims to provide a better understanding of how to properly …


Forensics Of Software Copyright Infringement Crimes: The Modern Posar Test Juxtaposed With The Dated Afc Test, Vinod P. Bhattathiripad Jan 2014

Forensics Of Software Copyright Infringement Crimes: The Modern Posar Test Juxtaposed With The Dated Afc Test, Vinod P. Bhattathiripad

Journal of Digital Forensics, Security and Law

This paper presents a new development in the forensics of software copyright through a juxtaposed comparison between the proven AFC test and the recent POSAR test, the two forensic procedures for establishing software copyright infringement cases. First, the paper separately overviews the 3-stage, linear sequential AFC test and then the 5-phase, cyclic POSAR test (as AFC’s logical extension). The paper then compares the processes involved in each of the 5 phases of the POSAR test with the processes involved in the 3 stages in the AFC test, for the benefit of forensic practitioners and researchers. Finally, the paper discusses some …


Fighting Child Pornography: A Review Of Legal And Technological Developments, Jasmine V. Eggestein, Kenneth J. Knapp Jan 2014

Fighting Child Pornography: A Review Of Legal And Technological Developments, Jasmine V. Eggestein, Kenneth J. Knapp

Journal of Digital Forensics, Security and Law

In our digitally connected world, the law is arguably behind the technological developments of the Internet age. While this causes many issues for law enforcement, it is of particular concern in the area of child pornography in the United States. With the wide availability of technologies such as digital cameras, peer-to-peer file sharing, strong encryption, Internet anonymizers and cloud computing, the creation and distribution of child pornography has become more widespread. Simultaneously, fighting the growth of this crime has become more difficult. This paper explores the development of both the legal and technological environments surrounding digital child pornography. In doing …


A Study Of Forensic Imaging In The Absence Of Write-Blockers, Gary C. Kessler, Gregory H. Carlton Jan 2014

A Study Of Forensic Imaging In The Absence Of Write-Blockers, Gary C. Kessler, Gregory H. Carlton

Journal of Digital Forensics, Security and Law

Best practices in digital forensics demand the use of write-blockers when creating forensic images of digital media, and this has been a core tenet of computer forensics training for decades. The practice is so ingrained that the integrity of images created without a write-blocker are immediately suspect. This paper describes a research framework that compares forensic images acquired with and without utilizing write-blockers in order to understand the extent of the differences, if any, in the resultant forensic copies. We specifically address whether differences are superficial or evidentiary, and we discuss the impact of admitting evidence acquired without write blocking. …


Automated Evaluation Of Approximate Matching Algorithms On Real Data, Frank Breitinger, Vassil Roussev Jan 2014

Automated Evaluation Of Approximate Matching Algorithms On Real Data, Frank Breitinger, Vassil Roussev

Electrical & Computer Engineering and Computer Science Faculty Publications

Bytewise approximate matching is a relatively new area within digital forensics, but its importance is growing quickly as practitioners are looking for fast methods to screen and analyze the increasing amounts of data in forensic investigations. The essential idea is to complement the use of cryptographic hash functions to detect data objects with bytewise identical representation with the capability to find objects with bytewise similarrepresentations.

Unlike cryptographic hash functions, which have been studied and tested for a long time, approximate matching ones are still in their early development stages and evaluation methodology is still evolving. Broadly, prior approaches have …


Non-Local Model For The Spatial Distribution Of Impact Ionization Events In Avalanche Photodiodes, David A. Ramirez, Majeed M. Hayat, Andrew S. Huntington, George M. Williams Jan 2014

Non-Local Model For The Spatial Distribution Of Impact Ionization Events In Avalanche Photodiodes, David A. Ramirez, Majeed M. Hayat, Andrew S. Huntington, George M. Williams

Electrical and Computer Engineering Faculty Research and Publications

We report an extension of the analytical dead space multiplication theory that provides the means to theoretically determine the spatial distribution of electron and hole impact-ionization events in an arbitrarily specified heterojunction multiplication region. The model can be used to understand the role of the dead space in regularizing the locations of impact ionization. It can also be utilized to analyze, design, and optimize new generations of ultra-low noise, multistaged gain avalanche photodiodes based upon judiciously energizing and relaxing carriers to enhance electron impact ionization and suppress hole impact ionization.


Robust And Resilient State-Dependent Control Of Continuous-Time Nonlinear Systems With General Performance Criteria, Xin Wang, Edwin E. Yaz, James Long Jan 2014

Robust And Resilient State-Dependent Control Of Continuous-Time Nonlinear Systems With General Performance Criteria, Xin Wang, Edwin E. Yaz, James Long

Electrical and Computer Engineering Faculty Research and Publications

A novel state-dependent control approach for continuous-time nonlinear systems with general performance criteria is presented in this paper. This controller is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state-dependent linear matrix inequality at each time, sufficient condition for the control solution can be found …


Statistical Approach For Determining Impulse Breakdown Voltage Distribution Under Dc Sweep Voltage, Mehmet Demi̇r, Celal Koraşli Jan 2014

Statistical Approach For Determining Impulse Breakdown Voltage Distribution Under Dc Sweep Voltage, Mehmet Demi̇r, Celal Koraşli

Turkish Journal of Electrical Engineering and Computer Sciences

This paper presents a comprehensive approach to the statistical characterization of impulse breakdown voltage under the effect of a DC sweep voltage. Several goodness-of-fit tests are applied to up-and-down test results obtained in the air-insulated rod-plane gap. Three distributions, normal, logistic, and Gumbel, are compared by means of the Kolmogorov--Smirnov goodness-of-fit test, and logistic distribution is also compared to 3-parameter Weibull distributions using the likelihood ratio test. Logistic distribution is found to be a possible alternative to normal and 3-parameter Weibull distributions.


A Learning Method To Evaluate A Generation Company's Bidding Strategy In The Electricity Market, Shengjie Yang, Jiangang Yao Jan 2014

A Learning Method To Evaluate A Generation Company's Bidding Strategy In The Electricity Market, Shengjie Yang, Jiangang Yao

Turkish Journal of Electrical Engineering and Computer Sciences

In the electricity market, generation companies (GenCos) are usually faced with the problem of choosing a better bidding strategy. They often have to evaluate each possible strategy according to its potential reward. In a competitive market environment, the electricity price is stochastic and volatile, and the GenCo's mixed strategies also make the problem more complicated. In this paper, we model the market price with a Markov regime-switching model and propose the temporal difference learning method in the Markov decision process to approximate the expected reward over an infinite horizon. The simulations based on this method have achieved the evaluation of …


Modeling And Simulation Of Deadbeat-Based Pi Controller In A Single-Phase H-Bridge Inverter For Stand-Alone Applications, Tow Leong Tiang, Dahaman Ishak Jan 2014

Modeling And Simulation Of Deadbeat-Based Pi Controller In A Single-Phase H-Bridge Inverter For Stand-Alone Applications, Tow Leong Tiang, Dahaman Ishak

Turkish Journal of Electrical Engineering and Computer Sciences

This paper presents a deadbeat-based proportional-integral (PI) controller for a stand-alone single-phase voltage source inverter using a battery cell as the primary energy source. The inverter system is simulated in MATLAB/Simulink. It consists of a lead acid battery, third-order Butterworth low-pass DC filter and AC filter, H-bridge inverter, step-up transformer, and a variety of loads, as well as its sinusoidal pulse-width modulation (SPWM) deadbeat-based PI controller. In this paper, 2 simulation case studies are carried out, which are the abrupt load changes from a 400 W resistive load to a 500 W resistive load, and from a 400 W resistive …


Hd-Mr: A New Algorithm For Number Recognition In Electrical Meters, Miguel Rodriguez, Geovanni Berdugo, Daladier Jabba, Maria Calle, Miguel Jimeno Jan 2014

Hd-Mr: A New Algorithm For Number Recognition In Electrical Meters, Miguel Rodriguez, Geovanni Berdugo, Daladier Jabba, Maria Calle, Miguel Jimeno

Turkish Journal of Electrical Engineering and Computer Sciences

Utility companies in developing countries employ analog electrical meters to determine consumption and bill their customers accordingly. Obtaining an accurate reading is an expensive and time-consuming process. High consumption levels of water, energy, or gas are fined by the government; thus, it is necessary to develop tools that allow users to be informed about their consumption in real time. This paper proposes a new number recognition algorithm named the Hausdorff distance for meter reading (HD-MR). Experiments prove that HD-MR can achieve a 99.9% recognition rate, even when recognized numbers are under rotation. The maximum recognition time is 31 ms; hence, …


A Novel Sms Application With Gsm Control On Numerator Systems, Ali̇ Sarikaş, Zi̇ya Ekşi̇, Cüneyt Yücelbaş, Ali̇ Buldu Jan 2014

A Novel Sms Application With Gsm Control On Numerator Systems, Ali̇ Sarikaş, Zi̇ya Ekşi̇, Cüneyt Yücelbaş, Ali̇ Buldu

Turkish Journal of Electrical Engineering and Computer Sciences

Numerator systems are widely used in various fields, sorting, and structures to ensure regular functioning. They are used today in places such as banks and hospitals to minimize the time spent waiting in a queue, and various studies have been undertaken to achieve efficiency in the workplace. At the beginning of these studies, numerator systems, which have been integrated into the short message service (SMS) application, have been used efficiently. With this application, to supply the required information to the user in the fastest way, a numerator system is developed by utilizing radio frequency communications and the SMS message structure. …


Adaptive Feedback Control For Linear Singular Systems, Azita Azarfar, Heydar Toossian Shandiz, Masoud Shafiee Jan 2014

Adaptive Feedback Control For Linear Singular Systems, Azita Azarfar, Heydar Toossian Shandiz, Masoud Shafiee

Turkish Journal of Electrical Engineering and Computer Sciences

An adaptive state feedback control approach for linear descriptor (or singular) systems is investigated in this paper, which makes the closed-loop dynamics of this class of systems regular, impulse-free, and stable. The proposed adaptive method is based on the Lyapunov theorem to ensure the admissibility of the descriptor system and it also provides the state tracking with the desired reference trajectory. First, a control law is generated to stabilize the equilibrium point of origin, and, after that, the method is extended to a state tracking controller. The presented controller not only gets the stable output tracking asymptotically but is also …


M-Fdbscan: A Multicore Density-Based Uncertain Data Clustering Algorithm, Atakan Erdem, Taflan İmre Gündem Jan 2014

M-Fdbscan: A Multicore Density-Based Uncertain Data Clustering Algorithm, Atakan Erdem, Taflan İmre Gündem

Turkish Journal of Electrical Engineering and Computer Sciences

In many data mining applications, we use a clustering algorithm on a large amount of uncertain data. In this paper, we adapt an uncertain data clustering algorithm called fast density-based spatial clustering of applications with noise (FDBSCAN) to multicore systems in order to have fast processing. The new algorithm, which we call multicore FDBSCAN (M-FDBSCAN), splits the data domain into c rectangular regions, where c is the number of cores in the system. The FDBSCAN algorithm is then applied to each rectangular region simultaneously. After the clustering operation is completed, semiclusters that occur during splitting are detected and merged to …


A Web Laboratory Using Matlab Builder Ne For Computer Image Processing, Sezgi̇n Kaçar, Cüneyt Bayilmiş, Özdemi̇r Çeti̇n Jan 2014

A Web Laboratory Using Matlab Builder Ne For Computer Image Processing, Sezgi̇n Kaçar, Cüneyt Bayilmiş, Özdemi̇r Çeti̇n

Turkish Journal of Electrical Engineering and Computer Sciences

Many various instruments are needed for computer image processing. These instruments are used for image restoration, analysis, etc. This paper presents a novel web laboratory based on MATLAB Builder NE with Web Figure, called ImageWeb, to facilitate computer image processing without needed technical information for users. The developed ImageWeb provides fundamental principles of image processing, including basic, compression, edge detection, filtering, optimization, and histogram processes, and so on. In addition, the usage of MATLAB Builder NE with MATLAB Web Figure provides high flexibility with visualization means such as zoom, rotate, and 3-dimensional view. Users can easily access ImageWeb using only …


Analysis Of A Rule-Based Curriculum Plan Optimization System With Spearman Rank Correlation, Di̇dem Abi̇di̇n, Hafi̇ze Şen Çakir Jan 2014

Analysis Of A Rule-Based Curriculum Plan Optimization System With Spearman Rank Correlation, Di̇dem Abi̇di̇n, Hafi̇ze Şen Çakir

Turkish Journal of Electrical Engineering and Computer Sciences

In corporations, accurate planning should be applied to manage the in-service training task within an optimum time period and without hindering the working tempo of the employees. For this reason, it is better to consider the curriculum planning task as a timetabling problem. However, when the timetables are prepared manually, it may turn out to be a complicated and time-consuming problem. In this study, it is aimed to evaluate the results of software introduced previously, which seeks to find a solution to the curriculum planning problem of in-service training programs in corporations using a rule-based genetic algorithm (GA). The input …


Effects Of A Current Transformer's Magnetizing Current On The Driving Voltage In Self-Oscillating Converters, Güngör Bal, Seli̇m Öncü Jan 2014

Effects Of A Current Transformer's Magnetizing Current On The Driving Voltage In Self-Oscillating Converters, Güngör Bal, Seli̇m Öncü

Turkish Journal of Electrical Engineering and Computer Sciences

Magnetizing inductance is one of the parameters that affect the phase and amplitude error of the output current of current transformers (CTs). In this study, the linear circuit model of a CT is developed to be used for driving purposes in power electronics applications. A simulation of the CT and its linear model is achieved. In the model circuit, the effect of the magnetizing inductance on the driving voltage can be examined. The equivalent circuit simulation results and the linear model simulation results along with the calculated results show agreement with each other. These results are compared with experimental results.


A New Approach In The Evaluation Of Hospital Information Systems, Güney Gürsel, Neşe Zayi̇m, Kemal Hakan Gülkesen, Ali̇ Ari̇foğlu, Osman Saka Jan 2014

A New Approach In The Evaluation Of Hospital Information Systems, Güney Gürsel, Neşe Zayi̇m, Kemal Hakan Gülkesen, Ali̇ Ari̇foğlu, Osman Saka

Turkish Journal of Electrical Engineering and Computer Sciences

Hospital information system (HIS) evaluation frameworks have largely been discussed in the literature. However, existing frameworks lack one important aspect: to what extent user expectations of HISs are met. In this study, user expectation data are collected by means of the 'expectation questionnaire'. The internal consistencies of the answers to the questionnaire are measured by Cronbach's alpha coefficient. Fuzzy logic methodologies are used to evaluate the expectation variables in the proposed evaluation framework. The evaluation variables are not represented in the results equally; they are reflected by the weights assigned by the users. Our proposed framework provides the overall degree …


Concurrently Attuned Design Of A Wadc-Based Upfc Psdc And Multiinput Pss For Improving Power System Dynamic Performance, Yashar Hashemi, Rasool Kazemzadeh, Mohammad Reza Azizian, Ahmad Sadeghi Yazdankhah Jan 2014

Concurrently Attuned Design Of A Wadc-Based Upfc Psdc And Multiinput Pss For Improving Power System Dynamic Performance, Yashar Hashemi, Rasool Kazemzadeh, Mohammad Reza Azizian, Ahmad Sadeghi Yazdankhah

Turkish Journal of Electrical Engineering and Computer Sciences

A new controller design for a unified power flow controller (UPFC) for damping of power system swings, focusing on interarea modes, is described in this paper. The proposed controller is a dual-layer controller, where the first layer is derived from local signals and the second layer is supplied by global signals, as additional measuring information from suitable remote network locations, where swings are well observable. For damping of low-frequency swing in wide-area operation, since there is little system information in the active power as input of the conventional power system stabilizer (CPSS), the effectiveness of the CPSS is low. For …


Current-Mode Universal Filter And Quadrature Oscillator Using Cdtas, Jie Jin, Chunhua Wang Jan 2014

Current-Mode Universal Filter And Quadrature Oscillator Using Cdtas, Jie Jin, Chunhua Wang

Turkish Journal of Electrical Engineering and Computer Sciences

A current differencing transconductance amplifier (CDTA)-based multiple-input single-output (MISO) current-mode universal filter and a quadrature oscillator (QO) are presented in this paper. The same circuit is used in the filter and oscillator, which only consists of 2 CDTAs and 2 capacitors. The universal filter can realize low-pass, high-pass, band-pass, band-stop, and all-pass biquad filter functions. With a slight modification of the filter, a new current-mode QO can be obtained easily. The natural frequency and quality factor of the filter and the conditions of oscillation and frequency of oscillation of the QO are all orthogonally adjustable through the bias currents of …


Design And Implementation Of A Programmable High-Voltage Impulse Measurement System, Serkan Dedeoğlu, Serhat Yilmaz Jan 2014

Design And Implementation Of A Programmable High-Voltage Impulse Measurement System, Serkan Dedeoğlu, Serhat Yilmaz

Turkish Journal of Electrical Engineering and Computer Sciences

High-voltage impulses (HVIs) are produced under laboratory conditions in order to emulate actual internal (switching) and external (lightning, thunderbolt) voltages. HVI resistance tests are essential to meet national and international standards on the production of electromechanical devices and materials, such as switchgears, and transformers that operate under these actual conditions. Accurate measurement of HVI is excessively difficult since the voltage level is so high, while the time parameters are relatively constricted. In this study, a reliable automatic HVI measuring and recording system, which accommodates a series of hardware and software designs in order to satisfy the constraints of the standards, …


Markovian Approach Applied To Reliability Modeling Of A Wind Farm, Mazaher Hajibashi, Akbar Ebrahimi Jan 2014

Markovian Approach Applied To Reliability Modeling Of A Wind Farm, Mazaher Hajibashi, Akbar Ebrahimi

Turkish Journal of Electrical Engineering and Computer Sciences

The exploitation of wind energy as a resource for generating electricity is going to make a leap forward. Large-scale wind farms (WFs) will be engaged with power systems in the near future and this will cause changes in the supply pattern. Wind speed has an intermittent behavior and the output power of a WF is highly variable, consistent with this fact. The Markov process could consider this characteristic of wind speed using the state transition rate probability matrix, an issue that is neglected when a probability distribution function is established to model the wind speed data. The adequacy indices of …