Back to the future: old methods for new estimation and test of the Gutenberg–Richter b-value for catalogues with variable completeness

2020 ◽  
Vol 224 (1) ◽  
pp. 337-339
Author(s):  
Matteo Taroni
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
B Value ◽  
Short Paper ◽  
Classical Approach ◽  
Testing Procedures ◽  
Single Level ◽  
Different Levels

SUMMARY In this short paper we show how to use the classical maximum likelihood estimation procedure for the b-value of the Gutenberg–Richter law for catalogues with different levels of completeness. With a simple correction, that is subtracting the relative completeness level to each magnitude, it becomes possible to use the classical approach. Moreover, this correction allows to adopt the testing procedures, initially made for catalogues with a single level of completeness, for catalogues with different levels of completeness too.

scholarly journals DECONVOLUTING PREFERENCES AND ERRORS: A MODEL FOR BINOMIAL PANEL DATA

2010 ◽  
Vol 26 (6) ◽  
pp. 1846-1854 ◽  
Author(s):  
Mogens Fosgerau ◽  
Søren Feodor Nielsen
Keyword(s):  
Maximum Likelihood ◽  
Panel Data ◽  
Maximum Likelihood Estimation ◽  
Unknown Parameter ◽  
Random Variables ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Choice Experiments ◽  
Stated Choice ◽  
Stated Choice Experiments

In many stated choice experiments researchers observe the random variablesVt,Xt, andYt= 1{U+δ⊤Xt+ εt<Vt},t≤T, whereδis an unknown parameter andUand εtare unobservable random variables. We show that under weak assumptions the distributions ofUand εtand also the unknown parameterδcan be consistently estimated using a sieved maximum likelihood estimation procedure.

scholarly journals Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Fan Yang ◽  
Hu Ren ◽  
Zhili Hu
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Evolutionary Strategy ◽  
Likelihood Method ◽  
Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

scholarly journals Full-Information Maximum Likelihood Estimation of Brand Positioning Maps Using Supermarket Scanning Data

1991 ◽  
Vol 28 (4) ◽  
pp. 483-490 ◽  
Author(s):  
Eric Waarts ◽  
Martin Carree ◽  
Berend Wierenga
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Full Information ◽  
Brand Positioning ◽  
Additional Advantage ◽  
Full Information Maximum Likelihood ◽  
Methodological Problems ◽  
Product Maps

The authors build on the idea put forward by Shugan to infer product maps from scanning data. They demonstrate that the actual estimation procedure used by Shugan has several methodological problems and may yield unstable estimates. They propose an alternative estimation procedure, full-information maximum likelihood (FIML), which addresses the problems and yields significantly improved results. An important additional advantage of the procedure is that the parameters of the preference distribution can be estimated simultaneously with the brand coordinates. Hence, it is not necessary to assume a fixed (uniform) distribution of preferences. An empirical application is presented in which the outcomes obtained from Shugan's procedure are compared with those from the proposed procedure.

scholarly journals The Exponentiated Burr XII Power Series Distribution: Properties and Applications

Stats ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 15-31
Author(s):  
Arslan Nasir ◽  
Haitham Yousof ◽  
Farrukh Jamal ◽  
Mustafa Korkmaz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Power Series ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Data Sets ◽  
Power Series Distributions ◽  
New Distribution

In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets.

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