scholarly journals Different Estimation Methods of the Stress-Strength Reliability Restricted Exponentiated Lomax Distribution

2021 ◽  
Vol 8 (3) ◽  
pp. 477-484
Author(s):  
Alaa M. Hamad ◽  
Bareq B. Salman
Keyword(s):  
Large Scale ◽  
Estimation Method ◽  
Least Square ◽  
Estimation Methods ◽  
Traffic Modeling ◽  
Actuarial Science ◽  
Lomax Distribution ◽  
Shrinkage Methods ◽  
Probabilistic Distribution ◽  
Queue Theory

Lomax distribution, a large-scale probabilistic distribution used in industry, economics, actuarial science, queue theory, and Internet traffic modeling, is the most important distribution in reliability theory. In this paper estimating the reliability of Restricted exponentiated Lomax distribution in two cases, when one component X strength and Y stress R=P(Y<X), and when system content two component series strength, Y stress by using different estimation method. such as maximum likelihood, least square and shrinkage methods. A comparison between the outcomes results of the applied methods has been carried out based on mean square error (MSE) to investigate the best method and the obtained results have been displayed via MATLAB software package.

scholarly journals A Comprehensive Review on Channel Estimation in OFDM System

2019 ◽  
Vol 5 (3) ◽  
pp. 6 ◽  
Author(s):  
Neha Dubey ◽  
Ankit Pandit
Keyword(s):  
Channel Estimation ◽  
Mean Square Error ◽  
Orthogonal Frequency Division Multiplexing ◽  
Transmission Rate ◽  
Minimum Mean Square Error ◽  
Estimation Method ◽  
Least Square ◽  
Estimation Methods ◽  
Mean Square ◽  
Mimo Ofdm

In wireless communication, orthogonal frequency division multiplexing (OFDM) plays a major role because of its high transmission rate. Channel estimation and tracking have many different techniques available in OFDM systems. Among them, the most important techniques are least square (LS) and minimum mean square error (MMSE). In least square channel estimation method, the process is simple but the major drawback is it has very high mean square error. Whereas, the performance of MMSE is superior to LS in low SNR, its main problem is it has high computational complexity. If the error is reduced to a very low value, then an exact signal will be received. In this paper an extensive review on different channel estimation methods used in MIMO-OFDM like pilot based, least square (LS) and minimum mean square error method (MMSE) and least minimum mean square error (LMMSE) methods and also other channel estimation methods used in MIMO-OFDM are discussed.

scholarly journals Estimating the Reliability Function of (2+1) Cascade Model

2019 ◽  
Vol 16 (2) ◽  
pp. 0395
Author(s):  
Khaleel Et al.
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Reliability Function ◽  
Cascade Model ◽  
Least Square ◽  
Estimation Methods ◽  
Percentage Error ◽  
Estimate Reliability ◽  
Best Estimator

This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.

scholarly journals Channel Estimation Based on Statistical Frames and Confidence Level in OFDM Systems

2018 ◽  
Vol 8 (9) ◽  
pp. 1607 ◽  
Author(s):  
Xiao Zhou ◽  
Chengyou Wang ◽  
Ruiguang Tang ◽  
Mingtong Zhang
Keyword(s):  
Channel Estimation ◽  
Mean Square Error ◽  
Confidence Level ◽  
Orthogonal Frequency Division Multiplexing ◽  
Minimum Mean Square Error ◽  
Estimation Method ◽  
Least Square ◽  
Estimation Methods ◽  
Mean Square ◽  
Inverse Operation

Channel estimation is an important module for improving the performance of the orthogonal frequency division multiplexing (OFDM) system. The pilot-based least square (LS) algorithm can improve the channel estimation accuracy and the symbol error rate (SER) performance of the communication system. In pilot-based channel estimation, a certain number of pilots are inserted at fixed intervals between OFDM symbols to estimate the initial channel information, and channel estimation results can be obtained by one-dimensional linear interpolation. The minimum mean square error (MMSE) and linear minimum mean square error (LMMSE) algorithms involve the inverse operation of the channel matrix. If the number of subcarriers increases, the dimension of the matrix becomes large. Therefore, the inverse operation is more complex. To overcome the disadvantages of the conventional channel estimation methods, this paper proposes a novel OFDM channel estimation method based on statistical frames and the confidence level. The noise variance in the estimated channel impulse response (CIR) can be largely reduced under statistical frames and the confidence level; therefore, it reduces the computational complexity and improves the accuracy of channel estimation. Simulation results verify the effectiveness of the proposed channel estimation method based on the confidence level in time-varying dynamic wireless channels.

scholarly journals Unification of Internal Resistance Estimation Methods for Li-Ion Batteries Using Hysteresis-Free Equivalent Circuit Models

Batteries ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 32
Author(s):  
S M Rakiul Islam ◽  
Sung-Yeul Park ◽  
Balakumar Balasingam
Keyword(s):  
Parameter Estimation ◽  
Equivalent Circuit ◽  
Electrochemical Impedance ◽  
Estimation Method ◽  
Equivalent Circuit Model ◽  
Parameter Extraction ◽  
Internal Resistance ◽  
Least Square ◽  
Estimation Methods ◽  
Li Ion

Internal resistance is one of the important parameters in the Li-Ion battery. This paper identifies it using two different methods: electrochemical impedance spectroscopy (EIS) and parameter estimation based on equivalent circuit model (ECM). Comparing internal resistance, the conventional parameter estimation method yields a different value than EIS. Therefore, a hysteresis-free parameter identification method based on ECM is proposed. The proposed technique separates hysteresis resistance from the effective resistance. It precisely estimated actual internal resistance, which matches the internal resistance obtained from EIS. In addition, state of charge, open circuit voltage, and different internal equivalent circuit components were identified. The least square method was used to identify the parameters based on ECM. A parameter extraction algorithm to interpret impedance spectrum obtained from the EIS. The algorithm is based on the properties of Nyquist plot, phasor algebra, and resonances. Experiments were conducted using a cellphone pouch battery and a cylindrical 18650 battery.

scholarly journals A Novel Robust Model Predictive Controller for Aerospace Three-Phase PWM Rectifiers

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2490 ◽  
Author(s):  
Tao Lei ◽  
Weiwei Tan ◽  
Guangsi Chen ◽  
Delin Kong
Keyword(s):  
Power System ◽  
Bayesian Estimation ◽  
Estimation Method ◽  
Parameters Estimation ◽  
Least Square ◽  
Estimation Methods ◽  
Control Performance ◽  
Least Square Estimation ◽  
Three Phase ◽  
Pwm Rectifiers

This paper presents a novel Model Predictive Direct Power Control (MPDPC) approach for the pulse width modulation (PWM) rectifiers in the Aircraft Alternating Current Variable Frequency (ACVF) power system. The control performance of rectifiers may be largely affected by variations in the AC side impedance, especially for systems with limited power volume system. A novel idea for estimating the impedance variation based on the Bayesian estimation, using an algorithm embedded in MPDPC is presented in this paper. The input filter inductance and its equivalent series resistance (ESR) of PWM rectifiers are estimated in this algorithm by measuring the input current and input voltage in each cycle with the probability Bayesian estimation theory. This novel estimation method can overcome the shortcomings of traditional data based estimation methods such as least square estimation (LSE), which achieves poor estimation results with the small samples data set. In ACVF systems, the effect on the parameters estimation accuracy caused by the number of sampling points in one cycle is also analyzed in detail by simulation. The validity of this method is verified by the digital and Hard-in-loop simulation compared with other estimation methods such as the least square estimation method. The experimental testing results show that the proposed estimation algorithm can improve the robustness and the control performance of the MPDPC under the condition of the uncertainty of the AC side parameters of the three-phase PWM rectifiers in aircraft electrical power system.

scholarly journals Robust Estimation methods of Generalized Exponential Distribution with Outliers

2020 ◽  
pp. 545-559
Author(s):  
Hisham Mohamed Almongy ◽  
Ehab M. Almetwally
Keyword(s):  
Robust Estimation ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Point Estimation ◽  
Least Square ◽  
Estimation Methods ◽  
Monte Carlo Simulation Study ◽  
Least Absolute Deviations ◽  
Complete Dataset ◽  
M Estimation

This paper discussed robust estimation for point estimation of the shape and scale parameters for generalized exponential (GE) distribution using a complete dataset in the presence of various percentages of outliers. In the case of outliers, it is known that classical methods such as maximum likelihood estimation (MLE), least square (LS) and maximum product spacing (MPS) in case of outliers cannot reach the best estimator. To confirm this fact, these classical methods were applied to the data of this study and compared with non-classical estimation methods. The non-classical (Robust) methods such as least absolute deviations (LAD), and M-estimation (using M. Huber (MH) weight and M. Bisquare (MB) weight) had been introduced to obtain the best estimation method for the parameters of the GE distribution. The comparison was done numerically by using the Monte Carlo simulation study. The two real datasets application confirmed that the M-estimation method is very much suitable for estimating the GE parameters. We concluded that the M-estimation method using Huber object function is a suitable estimation method in estimating the parameters of the GE distribution for a complete dataset in the presence of various percentages of outliers.

scholarly journals Continuous and Ordered Categorical Data in Network Psychometrics: Which Estimation Method to Choose? Deriving Guidelines for Applied Researchers

2021 ◽  
Author(s):  
Adela-Maria Isvoranu ◽  
Sacha Epskamp
Keyword(s):  
Categorical Data ◽  
Large Scale ◽  
Graphical Model ◽  
Large Body ◽  
Estimation Method ◽  
Psychological Research ◽  
Estimation Methods ◽  
Edge Weight ◽  
Ordered Categorical Data ◽  
Ordered Categorical

The Gaussian Graphical Model (GGM) has recently grown popular in psychological research, with a large body of estimation methods being proposed and discussed across various fields of study, and several algorithms being identified and recommend as applicable to psychological datasets. Such high-dimensional model estimation, however, is not trivial, and algorithms tend to perform differently in different settings. In addition, psychological research poses unique challenges, including placing a strong focus on weak edges (e.g., bridge edges), handling data measured on ordered scales, and relatively limited sample sizes. As a result, there is currently no consensus regarding which estimation procedure performs best in which setting. In this large-scale simulation study, we aimed to overcome this gap in the literature by comparing the performance of several estimation algorithms suitable for gaussian and skewed ordered categorical data across a multitude of settings, as to arrive at concrete guidelines from applied researchers. In total, we investigated 60 different metrics across 564,000 simulated datasets. We summarized our findings through a platform that allows for manually exploring simulation results. Overall, we found that an exchange between discovery (e.g., sensitivity, edge weight correlation) and caution (e.g., specificity, precision) should always be expected and achieving both¬—which is a requirement for perfect replicability—is difficult. Further, we identified that the estimation method is best chosen in light of each research question and highlighted, alongside desirable asymptotic properties and low sample size discovery, results according to most common research questions in the field.

A novel parameter estimation method for the Weibull distribution on heavily censored data

2019 ◽  
pp. 1748006X1988764 ◽  
Author(s):  
Renyan Jiang
Keyword(s):  
Parameter Estimation ◽  
Censored Data ◽  
Estimation Method ◽  
Least Square ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Distribution Models ◽  
Data Set ◽  
Hybrid Censoring ◽  
Parameter Estimation Method

It is desired to build the life distribution models of critical components (which are assumed to be non-repairable) of a repairable system as early as possible based on field failure data in order to optimize the operation and maintenance decisions of the components. When the number of the systems under observation is large and the observation duration is relatively short, the samples obtained for modeling are large and heavily censored. For such samples, the classical parameter estimation methods (e.g. maximum likelihood method and least square method) do not provide robust estimates. To address this issue, this article develops a hybrid censoring index to quantitatively describe censoring characteristics of a data set, proposes a novel parameter estimation method based on information extracted from censored observations, and evaluates the accuracy and robustness of the proposed method through a numerical experiment. Its applicable range in terms of the hybrid censoring index is determined through an accuracy analysis. The experiment results show that the proposed approach provides much accurate estimates than the classical methods for heavily censored data. A real-world example is also included.

scholarly journals Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1949
Author(s):  
Mukhtar M. Salah ◽  
M. El-Morshedy ◽  
M. S. Eliwa ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Least Square ◽  
Estimation Methods ◽  
Goodness Of Fit Test ◽  
Least Square Estimation ◽  
Chi Square ◽  
Anderson Darling ◽  
The Right

The extreme value theory is expanded by proposing and studying a new version of the Fréchet model. Some new bivariate type extensions using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula, and Renyi’s entropy copula are derived. After a quick study for its properties, different non-Bayesian estimation methods under uncensored schemes are considered, such as the maximum likelihood estimation method, Anderson–Darling estimation method, ordinary least square estimation method, Cramér–von-Mises estimation method, weighted least square estimation method, left-tail Anderson–Darling estimation method, and right-tail Anderson–Darling estimation method. Numerical simulations were performed for comparing the estimation methods using different sample sizes for three different combinations of parameters. The Barzilai–Borwein algorithm was employed via a simulation study. Three applications were presented for measuring the flexibility and the importance of the new model for comparing the competitive distributions under the uncensored scheme. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. The modified goodness-of-fit statistic test was applied for the right censored real data set, called leukemia free-survival times for autologous transplants. Based on the maximum likelihood estimators on initial data, the modified goodness-of-fit test recovered the loss in information while the grouping data and followed chi-square distributions. All elements of the modified goodness-of-fit criteria tests are explicitly derived and given.

scholarly journals Properties and Applications of the Modified Kies–Lomax Distribution with Estimation Methods

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Abdelaziz Alsubie
Keyword(s):  
Real Life ◽  
Estimation Method ◽  
Estimation Methods ◽  
Lomax Distribution ◽  
Estimation Algorithms ◽  
Real Life Data ◽  
Detailed Simulation ◽  
Relative Errors ◽  
Rival Models ◽  
Mean Square Errors

The present study introduces a new three-parameter model called the modified Kies–Lomax (MKL) distribution to extend the Lomax distribution and increase its flexibility in modeling real-life data. The MKL distribution, due to its flexibility, provides left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, unimodal, decreasing, and bathtub hazard rate shapes. The MKF density can be expressed as a linear mixture of Lomax densities. Some basic mathematical properties of the MKF model are derived. Its parameters are estimated via six estimation algorithms. We explore their performances using detailed simulation results, and the partial and overall ranks are provided for the measures of absolute biases, mean square errors, and mean relative errors to determine the best estimation method. The results show that the maximum product of spacings and maximum likelihood approaches are recommended to estimate the MKL parameters. Finally, the flexibility of the MKL distribution is checked using two real datasets, showing that it can provide close fit to both datasets as compared with other competing Lomax models. The three-parameter MKL model outperforms some four-parameter and five-parameter rival models.

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