scholarly journals Estimating parameters of linear regression with an exponential power distribution of errors by using a polynomial maximization method

2021 ◽  
Vol 1 (4 (109)) ◽  
pp. 64-73
Author(s):  
Serhii Zabolotnii ◽  
Vladyslav Khotunov ◽  
Anatolii Chepynoha ◽  
Olexandr Tkachenko
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Power Distribution ◽  
Maximum Likelihood Method ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Random Errors ◽  
Exponential Power Distribution ◽  
Exponential Power

This paper considers the application of a method for maximizing polynomials in order to find estimates of the parameters of a multifactorial linear regression provided the random errors of the regression model follow an exponential power distribution. The method used is conceptually close to a maximum likelihood method because it is based on the maximization of selective statistics in the neighborhood of the true values of the evaluated parameters. However, in contrast to the classical parametric approach, it employs a partial probabilistic description in the form of a limited number of statistics of higher orders. The adaptive algorithm of statistical estimation has been synthesized, which takes into consideration the properties of regression residues and makes it possible to find refined values for the estimates of the parameters of a linear multifactorial regression using the numerical Newton-Rafson iterative procedure. Based on the apparatus of the quantity of extracted information, the analytical expressions have been derived that make it possible to analyze the theoretical accuracy (asymptotic variances) of estimates for the method of maximizing polynomials depending on the magnitude of the exponential power distribution parameters. Statistical modeling was employed to perform a comparative analysis of the variance of estimates obtained using the method of maximizing polynomials with the accuracy of classical methods: the least squares and maximum likelihood. Regions of the greatest efficiency for each studied method have been constructed, depending on the magnitude of the parameter of the form of exponential power distribution and sample size. It has been shown that estimates from the polynomial maximization method may demonstrate a much lower variance compared to the estimates from a least-square method. And, in some cases (for flat-topped distributions and in the absence of a priori information), may exceed the estimates from the maximum likelihood method in terms of accuracy

scholarly journals A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling

2020 ◽  
Vol 8 (2) ◽  
pp. 610-630 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Emrah Altun EA ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Estimation Method ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Survival Times ◽  
New Model ◽  
Von Mises ◽  
Bootstrapping Method

In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the Maximum likelihood method, Cram er-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.

scholarly journals Generalized Exponential Power Distribution with Application to Complete and Censored Data

2021 ◽  
pp. 34-55
Author(s):  
M. M. E. Abd El-Monsef ◽  
M. M. El-Awady
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Power Distribution ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Type I ◽  
Sample Type ◽  
Exponential Power Distribution ◽  
Exponential Power

The exponential power distribution (EP) is a lifetime model that can exhibit increasing and bathtub hazard rate function. This paper proposed a generalization of EP distribution, named generalized exponential power (GEP) distribution. Some properties of GEP distribution will be investigated. Recurrence relations for single moments of generalized ordered statistics from GEP distribution are established and used for characterizing the GEP distribution. Estimation of the model parameters are derived using maximum likelihood method based on complete sample, type I, type II and random censored samples. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters. Three applications to real data, two with censored data, are provided in order to show the superiority of the proposed model to other models.

scholarly journals Stress-Strength Reliability for P(T

2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Ali Mutair ◽  
Nada Sabah Karam
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Pareto Distribution ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Method Of Moment ◽  
Important Conclusion ◽  
Large Samples ◽  
The Mean

In this paper, the reliability formula of the stress-strength model is derived for probability  of a component having strength X falling between two stresses T and Z, based on The New Weibull-Pareto Distribution with unknown parameter  and known and common parameters  and . Four methods for estimating the The New Weibull-Pareto parameters are discussed which are the Maximum Likelihood, Method of Moment, Least Square Method and Weighted Least Square Method, and the comparison between these estimations based on a simulation study by the mean square error criteria for each of the small, medium and large samples. The most important conclusion is that this comparison confirms that the performance of the maximum likelihood estimator works better for all experiments studied.

scholarly journals The Location-Scale Mixture Exponential Power Distribution: A Bayesian and Maximum Likelihood Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Z. Rahnamaei ◽  
N. Nematollahi ◽  
R. Farnoosh
Keyword(s):  
Maximum Likelihood ◽  
Power Distribution ◽  
Real Data ◽  
Scale Mixture ◽  
Exponential Power Distribution ◽  
Likelihood Approach ◽  
Slash Distribution ◽  
Exponential Power ◽  
Mean Square Errors ◽  
New Distribution

We introduce an alternative skew-slash distribution by using the scale mixture of the exponential power distribution. We derive the properties of this distribution and estimate its parameter by Maximum Likelihood and Bayesian methods. By a simulation study we compute the mentioned estimators and their mean square errors, and we provide an example on real data to demonstrate the modeling strength of the new distribution.

scholarly journals Estimasi Parameter Model Autoregressive dengan Metode Yule Walker, Least Square, dan Maximum Likelihood (Studi Kasus Data ROA BPRS di Indonesia)

2021 ◽  
Vol 1 (1) ◽  
pp. 1-6
Author(s):  
Maulida Nurhidayati
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Least Square ◽  
Likelihood Method ◽  
Model Parameters ◽  
Likelihood Methods ◽  
Simulation Data ◽  
Sample Data ◽  
Maximum Likelihood Methods ◽  
Modeling Data

The Autoregressive model is a time series univariate model for stationary models. In estimating parameters on this model can be done by several methods, namely yule-walker method, Least Square, and Maximum Likelihood. Each method has a different principle for estimating model parameters so that the results obtained will also be different. Based on this, in this study, the AR(1) model parameter estimation was estimated by generating data simulated 1000 times to see the performance of Yule-Walker, Least Square, and Maximum Likelihood methods. In addition, the comparison of these three methods is also done on ROA BPRS data that follows the AR(1) model. The results showed that the Maximum Likelihood method was able to provide mode results and comparison of the most suitable estimation results for simulation data and produce the smallest MAE values in the data in sample and MAPE, MSE, and MAE the smallest in the out sample data. These results show that the Maximum Likelihood method is the best method for modeling data that follows the AR(1) model.

scholarly journals Imputing missing distances in molecular phylogenetics

PeerJ ◽  
2018 ◽  
Vol 6 ◽  
pp. e5321 ◽  
Author(s):  
Xuhua Xia
Keyword(s):  
Phylogenetic Trees ◽  
Molecular Phylogenetics ◽  
Maximum Likelihood Method ◽  
Phylogenetic Reconstruction ◽  
Distance Matrix ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Multivariate Optimization ◽  
Tree Space

Missing data are frequently encountered in molecular phylogenetics, but there has been no accurate distance imputation method available for distance-based phylogenetic reconstruction. The general framework for distance imputation is to explore tree space and distance values to find an optimal combination of output tree and imputed distances. Here I develop a least-square method coupled with multivariate optimization to impute multiple missing distance in a distance matrix or from a set of aligned sequences with missing genes so that some sequences share no homologous sites (whose distances therefore need to be imputed). I show that phylogenetic trees can be inferred from distance matrices with about 10% of distances missing, and the accuracy of the resulting phylogenetic tree is almost as good as the tree from full information. The new method has the advantage over a recently published one in that it does not assume a molecular clock and is more accurate (comparable to maximum likelihood method based on simulated sequences). I have implemented the function in DAMBE software, which is freely available athttp://dambe.bio.uottawa.ca.

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