scholarly journals Statistical Inference for the Inverted Scale Family under General Progressive Type-II Censoring

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 731
Author(s):  
Jing Gao ◽  
Kehan Bai ◽  
Wenhao Gui
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Monte Carlo Simulations ◽  
Maximum Likelihood Estimator ◽  
Confidence Intervals ◽  
Interval Estimation ◽  
Bayesian Estimator ◽  
Small Samples ◽  
Likelihood Estimator ◽  
Scale Family

Two estimation problems are studied based on the general progressively censored samples, and the distributions from the inverted scale family (ISF) are considered as prospective life distributions. One is the exact interval estimation for the unknown parameter θ , which is achieved by constructing the pivotal quantity. Through Monte Carlo simulations, the average 90 % and 95 % confidence intervals are obtained, and the validity of the above interval estimation is illustrated with a numerical example. The other is the estimation of R = P ( Y < X ) in the case of ISF. The maximum likelihood estimator (MLE) as well as approximate maximum likelihood estimator (AMLE) is obtained, together with the corresponding R-symmetric asymptotic confidence intervals. With Bootstrap methods, we also propose two R-asymmetric confidence intervals, which have a good performance for small samples. Furthermore, assuming the scale parameters follow independent gamma priors, the Bayesian estimator as well as the HPD credible interval of R is thus acquired. Finally, we make an evaluation on the effectiveness of the proposed estimations through Monte Carlo simulations and provide an illustrative example of two real datasets.

scholarly journals When Was Westerhus Churchyard in Use?

2021 ◽  
Vol 13 (1) ◽  
pp. 161-182
Author(s):  
Claes-Henric Siven
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Monte Carlo Simulations ◽  
Maximum Likelihood Estimator ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Likelihood Estimator ◽  
Raw Data ◽  
Mass Graves ◽  
Point Estimates

The period of use for the Swedish medieval churchyard of Westerhus has been estimated by the maximum likelihood method. Raw data consist of 30 calibrated '4C-dates of some of the skeletons from the site. Bias and other properties of the maximum likelihood estimator are analyzed via a number of Monte Carlo simulations. The point estimates imply that the site was used in the period 1073-1356, that is, a somewhat longer period than previously assumed. The estimated length of the period of use affects the interpretation ofthe great number ofburied children. Population calculations lead to the conclusion that the six agglomerations of children's graves cannot be interpreted as mass graves.

A Hybrid Data Cloning Maximum Likelihood Estimator for Stochastic Volatility Models

2013 ◽  
Vol 5 (2) ◽  
pp. 193-229 ◽  
Author(s):  
Márcio Poletti Laurini
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Stochastic Volatility ◽  
Great Accuracy ◽  
Stochastic Volatility Models ◽  
Likelihood Estimator ◽  
Simulated Maximum Likelihood ◽  
Volatility Models ◽  
Data Cloning

Abstract: In this article, we analyze a maximum likelihood estimator using Data Cloning for Stochastic Volatility models. This estimator is constructed using a hybrid methodology based on Integrated Nested Laplace Approximations to calculate analytically the auxiliary Bayesian estimators with great accuracy and computational efficiency, without requiring the use of simulation methods such as Markov Chain Monte Carlo. We analyze the performance of this estimator compared to methods based on Monte Carlo simulations (Simulated Maximum Likelihood, MCMC Maximum Likelihood) and approximate maximum likelihood estimators using Laplace Approximations. The results indicate that this data cloning methodology achieves superior results over methods based on MCMC, comparable to results obtained by the Simulated Maximum Likelihood estimator. The methodology is extended to models with leverage effects, continuous time formulations, multifactor and multivariate stochastic volatility.

scholarly journals A New Maximum Likelihood Estimator Formulated in Pole-Residue Modal Model

2019 ◽  
Vol 9 (15) ◽  
pp. 3120
Author(s):  
Sandro Amador ◽  
Mahmoud El-Kafafy ◽  
Álvaro Cunha ◽  
Rune Brincker
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Maximum Likelihood Estimator ◽  
Confidence Intervals ◽  
Modal Parameters ◽  
Parameter Estimates ◽  
Modal Parameter ◽  
Likelihood Estimator ◽  
Pole Residue ◽  
Modal Model

Recently, a lot of efforts have been devoted to developing more precise Modal Parameter Estimation (MPE) techniques. This is explained by the necessity in civil, mechanical and aerospace engineering of obtaining accurate estimates for the modal parameters of the tested structures, as well as of determining reliable confidence intervals for these estimates. The Non-linear Least Squares (NLS) identification techniques based on Maximum Likelihood (ML) have been increasingly used in modal analysis to improve precision of estimates provided by the Least Squares (LS) based estimators when they are not accurate enough. Apart from providing more accurate estimates, the main advantage of the ML estimators, with regard to their LS counterparts, is that they allow for taking into account not only the measured Frequency Response Functions (FRFs) but also the noise information during the parametric identification process and, therefore, provide the modal parameters estimates together with their uncertainties bounds. In this paper, a new derivation of a Maximum Likelihood Estimator formulated in Pole-residue Modal Model (MLE-PMM) is presented. The proposed formulation is meant to be used in combination with the Least Squares Frequency Domain (LSCF) to improve the precision of the modal parameter estimates and compute their confidence intervals. Aiming at demonstrating the efficiency of the proposed approach, it is applied to two simulated examples in the final part of the paper.

scholarly journals Classical and Bayesian Inference of Conditional Stress-Strength Model under Kumaraswamy Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Fathy H. Riad ◽  
Mohammad Mehdi Saber ◽  
Mehrdad Taghipour ◽  
M. M. Abd El-Raouf
Keyword(s):  
Bayesian Inference ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Asymptotic Distribution ◽  
Confidence Intervals ◽  
Bootstrap Method ◽  
Strength Model ◽  
Likelihood Estimator ◽  
Kumaraswamy Distribution ◽  
Strength Models

Stress-strength models have been frequently studied in recent years. An applicable extension of these models is conditional stress-strength models. The maximum likelihood estimator of conditional stress-strength models, asymptotic distribution of this estimator, and its confidence intervals are obtained for Kumaraswamy distribution. In addition, Bayesian estimation and bootstrap method are applied to the model.

scholarly journals LARGE Estimation of the stress-strength reliability of progressively censored inverted exponentiated Rayleigh distributions

2017 ◽  
Vol 13 (1) ◽  
pp. 49-76 ◽  
Author(s):  
Akram Kohansal
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Scale Parameter ◽  
Sampling Technique ◽  
Credible Interval ◽  
Type Ii ◽  
Shape Parameters ◽  
Likelihood Estimator ◽  
Censored Samples

Abstract Based on progressively Type-II censored samples, this paper deals with the estimation of R = P(X < Y) when X and Y come from two independent inverted exponentiated rayleigh distributions with different shape parameters, but having the same scale parameter. The maximum likelihood estimator and UMVUE of R is obtained. Different confidence intervals are presented. The Bayes estimator of R and the corresponding credible interval using the Gibbs sampling technique are also proposed. Monte Carlo simulations are performed to compare the performances of the different methods. One illustrative example is provided to demonstrate the application of the proposed method.

Semiparametric efficient adaptive estimation of the GJR-GARCH model

2018 ◽  
Vol 35 (3-4) ◽  
pp. 141-160
Author(s):  
Nicola Ciccarelli
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Adaptive Estimation ◽  
Conditional Variance ◽  
Likelihood Estimator ◽  
Adaptive Estimator ◽  
Asymptotically Normal ◽  
Semiparametric Estimator ◽  
Quasi Maximum Likelihood

Abstract In this paper we derive a semiparametric efficient adaptive estimator for the GJR-GARCH {(1,1)} model. We first show that the quasi-maximum likelihood estimator is consistent and asymptotically normal for the model used in analysis, and we secondly derive a semiparametric estimator that is more efficient than the quasi-maximum likelihood estimator. Through Monte Carlo simulations, we show that the semiparametric estimator is adaptive for the parameters included in the conditional variance of the GJR-GARCH {(1,1)} model with respect to the unknown distribution of the innovation.

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