Bias and mean square error of the maximum likelihood estimators of the parameters of the intraclass correlation model

1997 ◽  
pp. 133-147
Author(s):  
Maia Berkane ◽  
Peter Bentler
Keyword(s):  
Maximum Likelihood ◽  
Mean Square Error ◽  
Intraclass Correlation ◽  
Maximum Likelihood Estimators ◽  
Mean Square ◽  
Correlation Model

Prediction Uncertainty in the Bornhuetter-Ferguson Claims Reserving Method: Revisited

2010 ◽  
Vol 5 (1) ◽  
pp. 7-17 ◽  
Author(s):  
D. H. Alai ◽  
M. Merz ◽  
M. V. Wüthrich
Keyword(s):  
Maximum Likelihood ◽  
Stochastic Model ◽  
Mean Square Error ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Maximum Likelihood Estimators ◽  
Model Parameters ◽  
Mean Square ◽  
Conditional Mean ◽  
Prediction Uncertainty

AbstractWe revisit the stochastic model of Alai et al. (2009) for the Bornhuetter-Ferguson claims reserving method, Bornhuetter & Ferguson (1972). We derive an estimator of its conditional mean square error of prediction (MSEP) using an approach that is based on generalized linear models and maximum likelihood estimators for the model parameters. This approach leads to simple formulas, which can easily be implemented in a spreadsheet.

scholarly journals اقتراح استعمال مبدأ اعظم دالة انتروبي POME على توزيع كاما العام في تقدير احتمالات البقاء للسكان في العراق

2016 ◽  
Vol 22 (93) ◽  
pp. 454
Author(s):  
عمر عبد المحسن علي ◽  
رغدة زياد طارق
Keyword(s):  
Maximum Likelihood ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Mean Square ◽  
Percent Error ◽  
Mean Absolute Percent Error ◽  
Generalized Gamma ◽  
Economic Survey ◽  
Absolute Percent Error

المستخلص: تم في هذا البحث تقدير دالة البقاء على قيد الحياة لبيانات تعاني من اضطراب وتشويش للمسح الاجتماعي والاقتصادي للأسرة في العراق 2012 (Iraq Household Socio-Economic Survey: IHSES II 2012) لبيانات فئات خماسية العمر تتبع توزيع كاما العام (Generalized Gamma: GG). واستعملت طريقتين للأغراض التقدير والموائمة fitting وهي طريقة مبدأ اعظم دالة انتروبي Principle of Maximizing Entropy: POME  وطريقة تمهيد لامعلمية بدالة لبّية Kernel ، للتغلب على المشاكل الرياضية التي تعتري التكاملات التي يتضمنها هذا التوزيع بالذات المتمثلة بتكامل دالة كاما الناقص، هذا الى جانب استعمال الطريقة التقليدية وهي الامكان الاعظم Maximum Likelihood: ML حيث تتم المقارنة على اساس اسلوب الجهاز المركزي للإحصاء في احتساب دالة البقاء من خلال برنامج MORTPAK كقيم حقيقية. وبعد ذلك القيام بالمقارنة باستعمال معيار جذر متوسط مربعات الخطأ Root Mean Square Error: RMSE  ، ومعيار متوسط مطلق نسبة الخطأ Mean Absolute Percent Error: MAPE  . وأظهرت النتائج أفضلية طريقة الانتروبي في تقدير دالة البقاء على الطرائق الاخرى.  

scholarly journals Best estimation for the Reliability of 2-parameter Weibull Distribution

2009 ◽  
Vol 6 (4) ◽  
pp. 705-710
Author(s):  
Baghdad Science Journal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Statistical Criterion ◽  
Mean Square ◽  
Simulation Process ◽  
The Mean ◽  
Two Parameter

This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

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 Data bank: nine numerical methods for determining the parameters of weibull for wind energy generation tested by five statistical tools

2021 ◽  
Vol 12 (2) ◽  
pp. 1114
Author(s):  
Ahmed Samir Badawi ◽  
Siti Hajar Yusoff ◽  
Alhareth Mohammed Zyoud ◽  
Sheroz Khan ◽  
Aisha Hashim ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Numerical Methods ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Prediction Accuracy ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Mean Square ◽  
Modified Maximum Likelihood

This study aims to determine the potential of wind energy in the mediterranean coastal plain of Palestine. The parameters of the Weibull distribution were calculated on basis of wind speed data. Accordingly, two approaches were employed: analysis of a set of actual time series data and theoretical Weibull probability function. In this analysis, the parameters Weibull shape factor ‘<em>k</em>’ and the Weibull scale factor ‘<em>c</em>’ were adopted. These suitability values were calculated using the following popular methods: method of moments (MM), standard deviation method (STDM), empirical method (EM), maximum likelihood method (MLM), modified maximum likelihood method (MMLM), second modified maximum likelihood method (SMMLM), graphical method (GM), least mean square method (LSM) and energy pattern factor method (EPF). The performance of these numerical methods was tested by root mean square error (RMSE), index of agreement (IA), Chi-square test (X<sup>2</sup>), mean absolute percentage error (MAPE) and relative root mean square error (RRMSE) to estimate the percentage of error. Among the prediction techniques. The EPF exhibited the greatest accuracy performance followed by MM and MLM, whereas the SMMLM exhibited the worst performance. The RMSE achieved the best prediction accuracy, whereas the RRMSE attained the worst prediction accuracy.

scholarly journals Combining Coded Signals with Arbitrary Modulations in Orthogonal Relay Channels

2008 ◽  
Vol 2008 ◽  
pp. 1-4 ◽  
Author(s):  
Brice Djeumou ◽  
Samson Lasaulce ◽  
Antoine O. Berthet
Keyword(s):  
Maximum Likelihood ◽  
Mean Square Error ◽  
Minimum Mean Square Error ◽  
Relay Channels ◽  
Mean Square ◽  
Relay Channel ◽  
Frequency Division ◽  
Decode And Forward ◽  
Convolutional Encoder

We consider a relay channel for which the following assumptions are made. (1) The source-destination and relay-destination channels are orthogonal (frequency division relay channel). (2) The relay implements the decode-and-forward protocol. (3) The source and relay implement the same channel encoder, namely, a convolutional encoder. (4) They can use arbitrary and possibly different modulations. In this framework, we derive the best combiner in the sense of the maximum likelihood (ML) at the destination and the branch metrics of the trellis associated with its channel decoder for the ML combiner and also for the maximum ratio combiner (MRC), cooperative-MRC (C-MRC), and the minimum mean-square error (MMSE) combiner.

New Testifying Method of Unit Weight Mean Square Error of No-Equal Precision Independent Surveying Values

2012 ◽  
Vol 170-173 ◽  
pp. 2904-2907 ◽  
Author(s):  
Yong He Deng
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Mean Square Error ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
New Method ◽  
Unit Weight ◽  
Mean Square ◽  
Maximum Likelihood Estimation Method

For unit weight mean square error of no-equal precision independent surveying values,this paper summed up several old estifying methods, pointed out their scarcities or mistakes, and advanced a sort of new method- maximum likelihood estimation method which is simple and strict.This is useful for theory of unit weight mean square error of no-equal precision independent surveying values to be perfect and for college surveying textbook to be improved and unified.

scholarly journals Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 62 ◽  
Author(s):  
Autcha Araveeporn
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Likelihood Function ◽  
Likelihood Method ◽  
Mean Square ◽  
Average Mean Square Error ◽  
Frequentist Method

This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero. The maximum likelihood method carries out the observed data to estimate the parameter of a probability distribution by maximizing a likelihood function under the statistical model, while this estimator is obtained by a differential parameter of the likelihood function. The efficiency of two methods is considered by average mean square error for simulation data, and mean square error for actual data. For simulation data, the data are generated at only the first-order models of the RCA model. The results have shown that the least-squares method performs better than the maximum likelihood. The average mean square error of the least-squares method shows the minimum values in all cases that indicated their performance. Finally, these methods are applied to the actual data. The series of monthly averages of the Stock Exchange of Thailand (SET) index and daily volume of the exchange rate of Baht/Dollar are considered to estimate and forecast based on the RCA model. The result shows that the least-squares method outperforms the maximum likelihood method.

Sign in / Sign up

Export Citation Format

Share Document