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 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 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 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.

scholarly journals Moment based Estimation for the Shape Parameters, Effect it on Some Probability Statistical Distributions Using the Moment Method and Maximum Likelihood Method

2020 ◽  
Vol 5 (6) ◽  
pp. 979-986
Author(s):  
Hassan Tawakol A. Fadol
Keyword(s):  
Maximum Likelihood ◽  
Shape Parameter ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Estimation Method ◽  
Simulation Method ◽  
Likelihood Method ◽  
Inductive Method ◽  
Binomial Distributions ◽  
Best Estimate

The purpose of this paper was to identify the values of the parameters of the shape of the binomial, bias one and natural distributions. Using the estimation method and maximum likelihood Method, the criterion of differentiation was used to estimate the shape parameter between the probability distributions and to arrive at the best estimate of the parameter of the shape when the sample sizes are small, medium, The problem was to find the best estimate of the characteristics of the society to be estimated so that they are close to the estimated average of the mean error squares and also the effect of the estimation method on estimating the shape parameter of the distributions at the sizes of different samples In the values of the different shape parameter, the descriptive and inductive method was selected in the analysis of the data by generating 1000 random numbers of different sizes using the simulation method through the MATLAB program. A number of results were reached, 10) to estimate the small shape parameter (0.3) for binomial distributions and Poisson and natural and they can use the Poisson distribution because it is the best among the distributions, and to estimate the parameter of figure (0.5), (0.7), (0.9) Because it is better for binomial binomial distributions, when the size of a sample (70) for a teacher estimate The small figure (0.3) of the binomial and boson distributions and natural distributions can be used for normal distribution because it is the best among the distributions.

scholarly journals A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Abdulhakim A. Al-babtain ◽  
I. Elbatal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Mathematical Properties

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

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 The Marshall-Olkin Modified Lindley Distribution: Properties and Applications

2020 ◽  
Author(s):  
Jiju Gillariose ◽  
Lishamol Tomy ◽  
Farrukh Jamal ◽  
Christophe Chesneau
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Lindley Distribution ◽  
New Model ◽  
Simulation Procedure ◽  
Recent Modification ◽  
New Distribution

This article is devoted to a new Marshall-Olkin distribution by using a recent modification of the Lindley distribution. Mathematical features of the new model are described. Utilizing maximum likelihood method, the parameters of the new model are estimated. Performance of the estimation approach is discussed by means of a simulation procedure. Moreover, applications of the new distribution are presented which reveal its superiority over other three competing Marshall-Olkin extended distributions of the literature.

scholarly journals Half-Logistic Xgamma Distribution: Properties and Estimation under Censored Samples

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Rashad Bantan ◽  
Amal S. Hassan ◽  
Mahmoud Elsehetry ◽  
B. M. Golam Kibria
Keyword(s):  
Maximum Likelihood ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Real Data ◽  
Least Square ◽  
Likelihood Method ◽  
Mean Residual Life ◽  
Model Parameters ◽  
Censored Samples ◽  
Von Mises

This paper proposed a new probability distribution, namely, the half-logistic xgamma (HLXG) distribution. Various statistical properties, such as, moments, incomplete moments, mean residual life, and stochastic ordering of the proposed distribution, are discussed. Parameter estimation of the half-logistic xgamma distribution is approached by the maximum likelihood method based on complete and censored samples. Asymptotic confidence intervals of model parameters are provided. A simulation study is conducted to illustrate the theoretical results. Moreover, the model parameters of the HLXG distribution are estimated by using the maximum likelihood, least square, maximum product spacing, percentile, and Cramer–von Mises (CVM) methods. Superiority of the new model over some existing distributions is illustrated through three real data sets.

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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