Maximum likelihood estimation of Lorenz curves using alternative parametric model

2004 ◽  
Vol 1 (1) ◽  
pp. 109-118
Author(s):  
Ibrahim M. Abdalla ◽  
Mohamed Y. Hassan
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Least Squares ◽  
Dirichlet Distribution ◽  
Likelihood Estimation ◽  
Parametric Models ◽  
Abu Dhabi ◽  
Parameter Estimates ◽  
Abu Dhabi Emirate ◽  
Least Squares Techniques

In this paper the Lorenz curve proposed by Abdalla and Hassan is fitted to grouped income data of Abu-Dhabi Emirate family expenditure survey, 1997, using Maximum likelihood estimation method and assuming that income shares follow a Dirichlet distribution. Employing Abdalla and Hassan's together with some known parametric Lorenz models, estimates based on the maximum likelihood are compared with those based on nonlinear least squares techniques. Given the nature of the distribution of income and the distinct characteristics of Abu-Dhabi Emirate, it is evident that the maximum likelihood estimation approach produces comparable parameter estimates to the non-linear least squares techniques, but higher standard errors and less goodness of fit. Under the two estimation techniques, the model proposed by Abdalla and Hassan performed well better than some well known parametric models in the literature.

Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution

2022 ◽  
Vol 7 (2) ◽  
pp. 2820-2839
Author(s):  
Saurabh L. Raikar ◽  
◽  
Dr. Rajesh S. Prabhu Gaonkar ◽  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Jaya Algorithm ◽  
Two Parameter

<abstract> <p>Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.</p> </abstract>

Bayesian Versus Maximum Likelihood Estimation of Treatment Effects in Bivariate Probit Instrumental Variable Models

2018 ◽  
Vol 7 (3) ◽  
pp. 651-659 ◽  
Author(s):  
Florian M. Hollenbach ◽  
Jacob M. Montgomery ◽  
Adriana Crespo-Tenorio
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Instrumental Variable ◽  
Likelihood Estimation ◽  
Direct Calculation ◽  
Causal Effects ◽  
Parameter Estimates ◽  
Bivariate Probit ◽  
Probit Models ◽  
Quantities Of Interest

Bivariate probit models are a common choice for scholars wishing to estimate causal effects in instrumental variable models where both the treatment and outcome are binary. However, standard maximum likelihood approaches for estimating bivariate probit models are problematic. Numerical routines in popular software suites frequently generate inaccurate parameter estimates and even estimated correctly, maximum likelihood routines provide no straightforward way to produce estimates of uncertainty for causal quantities of interest. In this note, we show that adopting a Bayesian approach provides more accurate estimates of key parameters and facilitates the direct calculation of causal quantities along with their attendant measures of uncertainty.

scholarly journals "Evaluation of Some Methods for Estimating the Weibull Distribution Parameters"

2017 ◽  
Vol 4 (2) ◽  
pp. 8-14
Author(s):  
J. A. Labban ◽  
H. H. Depheal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Mean Square Error ◽  
Random Sample ◽  
Likelihood Estimation ◽  
Mean Square ◽  
Distribution Parameters

"This paper some of different methods to estimate the parameters of the 2-Paramaters Weibull distribution such as (Maximum likelihood Estimation, Moments, Least Squares, Term Omission). Mean square error will be considered to compare methods fits in case to select the best one. There by simulation will be implemented to generate different random sample of the 2-parameters Weibull distribution, those contain (n=10, 50, 100, 200) iteration each 1000 times."

scholarly journals A New Online Calibration Method Based on Lord’s Bias-Correction

2017 ◽  
Vol 41 (6) ◽  
pp. 456-471 ◽  
Author(s):  
Yinhong He ◽  
Ping Chen ◽  
Yong Li ◽  
Shumei Zhang
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Bias Correction ◽  
Likelihood Estimation ◽  
Calibration Method ◽  
New Method ◽  
Parameter Estimates ◽  
Item Calibration ◽  
Online Calibration ◽  
True Values

Online calibration technique has been widely employed to calibrate new items due to its advantages. Method A is the simplest online calibration method and has attracted many attentions from researchers recently. However, a key assumption of Method A is that it treats person-parameter estimates [Formula: see text] (obtained by maximum likelihood estimation [MLE]) as their true values [Formula: see text], thus the deviation of the estimated [Formula: see text] from their true values might yield inaccurate item calibration when the deviation is nonignorable. To improve the performance of Method A, a new method, MLE-LBCI-Method A, is proposed. This new method combines a modified Lord’s bias-correction method (named as maximum likelihood estimation-Lord’s bias-correction with iteration [MLE-LBCI]) with the original Method A in an effort to correct the deviation of [Formula: see text] which may adversely affect the item calibration precision. Two simulation studies were carried out to explore the performance of both MLE-LBCI and MLE-LBCI-Method A under several scenarios. Simulation results showed that MLE-LBCI could make a significant improvement over the ML ability estimates, and MLE-LBCI-Method A did outperform Method A in almost all experimental conditions.

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