scholarly journals A New Quantile Estimation Method of Weibull-Rayleigh Distribution

2020 ◽  
pp. 28-37
Author(s):  
A. S. Ogunsanya ◽  
E. E. E. Akarawak ◽  
W. B. Yahya
Keyword(s):  
Parameter Estimation ◽  
Estimation Method ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Absolute Error ◽  
Rayleigh Distribution ◽  
Least Square ◽  
Estimation Methods ◽  
Data Set ◽  
Total Deviation

In this paper, we compared different Parameter Estimation method of the two parameter Weibull-Rayleigh Distribution (W-RD) namely; Maximum Likelihood Estimation (MLE), Least Square Estimation method (LSE) and three methods of Quartile Estimators. Two of the quartile methods have been applied in literature, while the third method (Q1-M) is introduced in this work. The methods have been applied to simulate data. These methods of estimation were compared using Error, Mean Square Error and Total Deviation (TD) which is also known as Sum Absolute Error Estimate (SAEE). The analytical results show that the performances of all the parameter estimation methods were satisfactory with data set of Weibull-Rayleigh distribution while degree of accuracy is determined by the sample size. The proposed quartile (Q1-M) method has the least Total Deviation and MSE. In addition, the quartile methods perform better than MLE for the simulated data. In particular, the proposed quartile methods (Q1-M) have an added advantage of simplicity in usage than MLE methods.

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 HALF LOGISTIC MODIFIED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS

2020 ◽  
pp. 276-287
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Type I ◽  
Data Set ◽  
Von Mises

In this study, we have introduced a three-parameter probabilistic model established from type I half logistic-Generating family called half logistic modified exponential distribution. The mathematical and statistical properties of this distribution are also explored. The behavior of probability density, hazard rate, and quantile functions are investigated. The model parameters are estimated using the three well known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises estimation (CVME) methods. Further, we have taken a real data set and verified that the presented model is quite useful and more flexible for dealing with a real data set. KEYWORDS— Half-logistic distribution, Estimation, CVME ,LSE, , MLE

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 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 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 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 Multi-Scene Building Height Estimation Method Based on Shadow in High Resolution Imagery

2021 ◽  
Vol 13 (15) ◽  
pp. 2862
Author(s):  
Yakun Xie ◽  
Dejun Feng ◽  
Sifan Xiong ◽  
Jun Zhu ◽  
Yangge Liu
Keyword(s):  
Remote Sensing ◽  
High Resolution ◽  
Estimation Method ◽  
Absolute Error ◽  
Large Error ◽  
Estimation Methods ◽  
Height Estimation ◽  
Building Height ◽  
Remote Sensing Imagery ◽  
High Resolution Imagery

Accurately building height estimation from remote sensing imagery is an important and challenging task. However, the existing shadow-based building height estimation methods have large errors due to the complex environment in remote sensing imagery. In this paper, we propose a multi-scene building height estimation method based on shadow in high resolution imagery. First, the shadow of building is classified and described by analyzing the features of building shadow in remote sensing imagery. Second, a variety of shadow-based building height estimation models is established in different scenes. In addition, a method of shadow regularization extraction is proposed, which can solve the problem of mutual adhesion shadows in dense building areas effectively. Finally, we propose a method for shadow length calculation combines with the fish net and the pauta criterion, which means that the large error caused by the complex shape of building shadow can be avoided. Multi-scene areas are selected for experimental analysis to prove the validity of our method. The experiment results show that the accuracy rate is as high as 96% within 2 m of absolute error of our method. In addition, we compared our proposed approach with the existing methods, and the results show that the absolute error of our method are reduced by 1.24 m-3.76 m, which can achieve high-precision estimation of building height.

scholarly journals Construction of a Genetic Linkage Map in Tetraploid Species Using Molecular Markers

Genetics ◽  
2001 ◽  
Vol 157 (3) ◽  
pp. 1369-1385 ◽  
Author(s):  
Z W Luo ◽  
C A Hackett ◽  
J E Bradshaw ◽  
J W McNicol ◽  
D Milbourne
Keyword(s):  
Molecular Markers ◽  
Linkage Map ◽  
Recombination Frequency ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Lod Score ◽  
Data Set ◽  
Independent Segregation ◽  
The Em Algorithm ◽  
Small Set

Abstract This article presents methodology for the construction of a linkage map in an autotetraploid species, using either codominant or dominant molecular markers scored on two parents and their full-sib progeny. The steps of the analysis are as follows: identification of parental genotypes from the parental and offspring phenotypes; testing for independent segregation of markers; partition of markers into linkage groups using cluster analysis; maximum-likelihood estimation of the phase, recombination frequency, and LOD score for all pairs of markers in the same linkage group using the EM algorithm; ordering the markers and estimating distances between them; and reconstructing their linkage phases. The information from different marker configurations about the recombination frequency is examined and found to vary considerably, depending on the number of different alleles, the number of alleles shared by the parents, and the phase of the markers. The methods are applied to a simulated data set and to a small set of SSR and AFLP markers scored in a full-sib population of tetraploid potato.

Utilizarea teoriei valorilor extreme în climatologie

2019 ◽  
Author(s):  
Valentin Raileanu ◽  
Keyword(s):  
Maximum Likelihood ◽  
Extreme Values ◽  
Probability Distributions ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
R Software ◽  
Data Set ◽  
Data Format ◽  
Generalized Pareto ◽  
Distribution Parameters

The article briefly describes the history and fields of application of the theory of extreme values, including climatology. The data format, the Generalized Extreme Value (GEV) probability distributions with Bock Maxima, the Generalized Pareto (GP) distributions with Point of Threshold (POT) and the analysis methods are presented. Estimating the distribution parameters is done using the Maximum Likelihood Estimation (MLE) method. Free R software installation, the minimum set of required commands and the GUI in2extRemes graphical package are described. As an example, the results of the GEV analysis of a simulated data set in in2extRemes are presented.

scholarly journals New Lindley Half Cauchy Distribution: Theory and Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 1-7
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Cauchy Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

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