Using Approximation Non-Bayesian Computation with Fuzzy Data to Estimation Inverse Weibull Parameters and Reliability Function

2018 ◽  
pp. 397
Author(s):  
Nadia Hashim Al-Noor ◽  
Shurooq A.K. Al-Sultany
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Mean Squared Error ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Fuzzy Data ◽  
Monte Carlo Simulation Study ◽  
Weibull Parameters ◽  
Squared Error ◽  
Newton Raphson

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function in terms of their mean squared error values and integrated mean squared error values respectively.

Estimating an Autoregressive Current Effects Model of Sales Response when Observations are Aggregated over Time: Least Squares versus Maximum Likelihood

1988 ◽  
Vol 25 (3) ◽  
pp. 301-307
Author(s):  
Wilfried R. Vanhonacker
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Serial Correlation ◽  
Mean Squared Error ◽  
Generalized Least Squares ◽  
Parameter Estimates ◽  
Squared Error ◽  
Positive Serial Correlation ◽  
Serial Correlation Coefficient ◽  
Over Time

Estimating autoregressive current effects models is not straightforward when observations are aggregated over time. The author evaluates a familiar iterative generalized least squares (IGLS) approach and contrasts it to a maximum likelihood (ML) approach. Analytic and numerical results suggest that (1) IGLS and ML provide good estimates for the response parameters in instances of positive serial correlation, (2) ML provides superior (in mean squared error) estimates for the serial correlation coefficient, and (3) IGLS might have difficulty in deriving parameter estimates in instances of negative serial correlation.

Inadmissibility of the Maximum Likelihood Estimator in the Presence of Prior Information

1970 ◽  
Vol 13 (3) ◽  
pp. 391-393 ◽  
Author(s):  
B. K. Kale
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Loss Function ◽  
Prior Information ◽  
Mean Squared Error ◽  
Closed Interval ◽  
Likelihood Estimator ◽  
Usual Estimator ◽  
Squared Error

Lehmann [1] in his lecture notes on estimation shows that for estimating the unknown mean of a normal distribution, N(θ, 1), the usual estimator is neither minimax nor admissible if it is known that θ belongs to a finite closed interval [a, b] and the loss function is squared error. It is shown that , the maximum likelihood estimator (MLE) of θ, has uniformly smaller mean squared error (MSE) than that of . It is natural to ask the question whether the MLE of θ in N(θ, 1) is admissible or not if it is known that θ ∊ [a, b]. The answer turns out to be negative and the purpose of this note is to present this result in a slightly generalized form.

Finite Sample Properties of Several Predictors From an Autoregressive Model

1987 ◽  
Vol 3 (3) ◽  
pp. 359-370 ◽  
Author(s):  
Koichi Maekawa
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Asymptotic Expansions ◽  
Autoregressive Model ◽  
Mean Squared Error ◽  
The Other ◽  
Finite Sample ◽  
Squared Error ◽  
Distributional Properties ◽  
Finite Sample Properties

We compare the distributional properties of the four predictors commonly used in practice. They are based on the maximum likelihood, two types of the least squared, and the Yule-Walker estimators. The asymptotic expansions of the distribution, bias, and mean-squared error for the four predictors are derived up to O(T−1), where T is the sample size. Examining the formulas of the asymptotic expansions, we find that except for the Yule-Walker type predictor, the other three predictors have the same distributional properties up to O(T−1).

scholarly journals Estimation procedures on Type-II censored data from a scaled Muth distribution

2021 ◽  
pp. 148-158
Author(s):  
Hayrinisa Demirci BIÇER
Keyword(s):  
Censored Data ◽  
Mean Squared Error ◽  
Real Life ◽  
Model Parameters ◽  
Type Ii ◽  
Monte Carlo Simulation Study ◽  
Anal Ysis ◽  
Squared Error ◽  
Type Ii Censored Data ◽  
Censoring Scheme

In the present paper, we consider the estimation problem for the scaled Muth distribution under Type-II censoring scheme. In order to estimate the model parameters α and β, the maximum likelihood, the least-squares, and the maximum spacing estimators are derived. To show estimation efficiencies of the estimators obtained with this paper, we present an exten- sive Monte-Carlo simulation study in which the estimators are compared according to bias and mean squared error criteria. Furthermore, we evaluate the applicability of the scaled Muth distribution by taking into account both full and Type-II censored data situations by an anal- ysis conducted on a real-life dataset.

Estimation of Weibull Parameters Using Fractional Moments

1984 ◽  
Vol 33 (3-4) ◽  
pp. 179-186 ◽  
Author(s):  
S.P. Mukherjee ◽  
B.C. Sasmal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Relative Efficiency ◽  
Maximum Likelihood Estimators ◽  
Weibull Parameters ◽  
Moment Estimators ◽  
Fractional Moments ◽  
Distribution Moment ◽  
The Moment ◽  
Two Parameter

For a two-parameter Weibull distribution, moment estimators of the parameters have been developed by choosing orders of two moments (allowing fractions) so that the overall relative efficiency of the moment estimators compared with the maximum likelihood estimators is maximized . Some calculations in support of the superiority of fractional moments over integer moments in this connection have also been presented.

Record-Based Estimators for Weibull Distribution

2014 ◽  
Vol 14 (07) ◽  
pp. 1450026 ◽  
Author(s):  
Mahdi Teimouri ◽  
Saralees Nadarajah
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Likelihood Estimation ◽  
Record Values ◽  
Likelihood Estimator ◽  
Squared Error ◽  
Upper Record Values ◽  
Upper Record

Teimouri and Nadarajah [Statist. Methodol.13 (2013) 12–24] considered bias corrected maximum likelihood estimation of the Weibull distribution based on upper record values. Here, we propose an estimator for the Weibull shape parameter based on consecutive upper records. It is shown by simulations that the proposed estimator has less bias and less mean squared error than an estimator due to Soliman et al. [Comput. Statist. Data Anal.51 (2006) 2065–2077] based on all upper records. Also, the proposed estimator can be considered as a good competitor for the maximum likelihood estimator of the shape parameter based on complete data. This is proved by simulations and using a real dataset.

Parametric estimation and inference

2019 ◽  
pp. 165-185
Author(s):  
M. D. Edge
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Function ◽  
Maximum Likelihood Estimators ◽  
Wald Test ◽  
Parametric Model ◽  
Parametric Estimation ◽  
Ratio Test ◽  
Sampling Variance ◽  
Squared Error Loss Function ◽  
Squared Error

If it is reasonable to assume that the data are generated by a fully parametric model, then maximum-likelihood approaches to estimation and inference have many appealing properties. Maximum-likelihood estimators are obtained by identifying parameters that maximize the likelihood function, which can be done using calculus or using numerical approaches. Such estimators are consistent, and if the costs of errors in estimation are described by a squared-error loss function, then they are also efficient compared with their consistent competitors. The sampling variance of a maximum-likelihood estimate can be estimated in various ways. As always, one possibility is the bootstrap. In many models, the variance of the maximum-likelihood estimator can be derived directly once its form is known. A third approach is to rely on general properties of maximum-likelihood estimators and use the Fisher information. Similarly, there are many ways to test hypotheses about parameters estimated by maximum likelihood. This chapter discusses the Wald test, which relies on the fact that the sampling distribution of maximum-likelihood estimators is normal in large samples, and the likelihood-ratio test, which is a general approach for testing hypotheses relating nested pairs of models.

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