scholarly journals PERBANDINGAN ESTIMASI KEMAMPUAN LATEN ANTARA METODE MAKSIMUM LIKELIHOOD DAN METODE BAYES

2015 ◽  
Vol 19 (2) ◽  
pp. 145-155 ◽  
Author(s):  
Heri Retnawati
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Latent Trait ◽  
Estimation Method ◽  
Simulation Method ◽  
Likelihood Method ◽  
Mean Square ◽  
Bayes Methods ◽  
National Examination ◽  
Latent Traits

Studi ini bertujuan untuk membandingkan ketepatan estimasi kemampuan laten (latent trait) pada model logistik dengan metode maksimum likelihood (ML) gabungan dan bayes. Studi ini menggunakan metode simulasi Monte Carlo, dengan model data ujian nasional matematika SMP. Variabel simulasi adalah panjang tes dan banyaknya peserta.  Data dibangkitkan dengan menggunakan SAS/IML dengan replikasi 40 kali, dan tiap data diestimasi dengan ML dan Bayes. Hasil estimasi kemudian dibandingkan dengan kemampuan yang sebenarnya, dengan menghitung mean square of error (MSE) dan korelasi antara kemampuan laten yang sebenarnya dan hasil estimasi. Metode yang memiliki MSE lebih kecil dikatakan sebagai metode estimasi yang lebih baik. Hasil studi menunjukkan bahwa pada estimasi kemampuan laten dengan 15, 20, 25, dan 30 butir dengan 500 dan 1.000 peserta, hasil MSE belum stabil, namun ketika peserta menjadi 1.500 orang, diperoleh akurasi estimasi kemampuan yang hampir sama baik estimasi antara metode ML dan metode Bayes. Pada estimasi dengan 15 dan 20 butir dan peserta 500, 1.000, dan 1.500, hasil MSE belum stabil, dan ketika estimasi melibatkan 25 dan 30 butir, baik dengan peserta 500, 1.000, maupun 1.500 akan diperoleh hasil yang lebih akurat dengan metode ML. Kata kunci: estimasi kemampuan, metode maksimum likelihood, metode Bayes     THE COMPARISON OF ESTIMATION OF LATENT TRAITS USING MAXIMUM LIKELIHOOD AND BAYES METHODS Abstract This study aimed to compare the accuracy of the estimation of latent ability (latent trait) in the logistic model using maximum likelihood (ML) and Bayes methods. This study uses a quantitative approach that is the Monte Carlo simulation method using students responses to national examination as data model, and variables are the length of the test and the number of participants. The data were generated using SAS/IML with replication 40 times, and each datum is then estimated by ML and Bayes. The estimation results are then compared with the true abilities, by calculating the mean square of error (MSE) and correlation between the true ability and the results of estimation. The smaller MSE estimation method is said to be better. The study shows that on the estimates with 15, 20, 25, and 30 items with 500 and 1,000 participants, the results have not been stable, but when participants were upto 1,500 people, it was obtained accuracy estimation capabilities similar to the ML and Bayesian methods, and with 15 items and participants of 500, 1,000, and 1,500, the result has not been stable, while using 20 items, the results have not been stable, and when estimates involve 25 and 30 items, either by participants 500, 1,000, and 1,500 it will obtain more accurate results with ML method. Keywords: estimation ability, maximum likelihood method, bayes method

scholarly journals Moment based Estimation for the Shape Parameters, Effect it on Some Probability Statistical Distributions Using the Moment Method and Maximum Likelihood Method

2020 ◽  
Vol 5 (6) ◽  
pp. 979-986
Author(s):  
Hassan Tawakol A. Fadol
Keyword(s):  
Maximum Likelihood ◽  
Shape Parameter ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Estimation Method ◽  
Simulation Method ◽  
Likelihood Method ◽  
Inductive Method ◽  
Binomial Distributions ◽  
Best Estimate

The purpose of this paper was to identify the values of the parameters of the shape of the binomial, bias one and natural distributions. Using the estimation method and maximum likelihood Method, the criterion of differentiation was used to estimate the shape parameter between the probability distributions and to arrive at the best estimate of the parameter of the shape when the sample sizes are small, medium, The problem was to find the best estimate of the characteristics of the society to be estimated so that they are close to the estimated average of the mean error squares and also the effect of the estimation method on estimating the shape parameter of the distributions at the sizes of different samples In the values of the different shape parameter, the descriptive and inductive method was selected in the analysis of the data by generating 1000 random numbers of different sizes using the simulation method through the MATLAB program. A number of results were reached, 10) to estimate the small shape parameter (0.3) for binomial distributions and Poisson and natural and they can use the Poisson distribution because it is the best among the distributions, and to estimate the parameter of figure (0.5), (0.7), (0.9) Because it is better for binomial binomial distributions, when the size of a sample (70) for a teacher estimate The small figure (0.3) of the binomial and boson distributions and natural distributions can be used for normal distribution because it is the best among the distributions.

ON THE PROPERTIES AND MLEs OF GENERALIZED ODD GENERALIZED EXPONENTIAL- EXPONENTIAL DISTRIBUTION

2021 ◽  
Vol 4 (4) ◽  
pp. 155-165
Author(s):  
Aminu Suleiman Mohammed ◽  
Badamasi Abba ◽  
Abubakar G. Musa
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Estimation Method ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Lifetime Data ◽  
Failure Rates ◽  
Simulation Experiments

For proper actualization of the phenomenon contained in some lifetime data sets, a generalization, extension or modification of classical distributions is required. In this paper, we introduce a new generalization of exponential distribution, called the generalized odd generalized exponential-exponential distribution. The proposed distribution can model lifetime data with different failure rates, including the increasing, decreasing, unimodal, bathtub, and decreasing-increasing-decreasing failure rates. Various properties of the model such as quantile function, moment, mean deviations, Renyi entropy, and order statistics.  We provide an approximation for the values of the mean, variance, skewness, kurtosis, and mean deviations using Monte Carlo simulation experiments. Estimating of the distribution parameters is performed using the maximum likelihood method, and Monte Carlo simulation experiments is used to assess the estimation method. The method of maximum likelihood is shown to provide a promising parameter estimates, and hence can be adopted in practice for estimating the parameters of the distribution. An application to real and simulated datasets indicated that the new model is superior to the fits than the other compared distributions

scholarly journals Selection of Efficient Parameter Estimation Method for Two-Parameter Weibull Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Mohammed M. A. Almazah ◽  
Muhammad Ismail
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Estimation Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Mean Square ◽  
Two Parameter

Several studies have considered various scheduling methods and reliability functions to determine the optimum maintenance time. These methods and functions correspond to the lowest cost by using the maximum likelihood estimator to evaluate the model parameters. However, this paper aims to estimate the parameters of the two-parameter Weibull distribution (α, β). The maximum likelihood estimation method, modified linear exponential loss function, and Wyatt-based regression method are used for the estimation of the parameters. Minimum mean square error (MSE) criterion is used to evaluate the relative efficiency of the estimators. The comparison of the different parameter estimation methods is conducted, and the efficiency of these methods is observed, both mathematically and experimentally. The simulation study is conducted for comparison of samples sizes (10, 50, 100, 150) based on the mean square error (MSE). It is concluded that the maximum likelihood method was found to be the most efficient method for all sample sizes used in the research because it achieved the least MSE compared with other methods.

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 Detecting long-memory: Monte Carlo simulations and application to daily streamflow processes

2006 ◽  
Vol 3 (4) ◽  
pp. 1603-1627 ◽  
Author(s):  
W. Wang ◽  
P. H. A. J. M. van Gelder ◽  
J. K. Vrijling ◽  
X. Chen
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Long Memory ◽  
Positive Relationship ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Large Data ◽  
Daily Streamflow ◽  
Maximum Likelihood Estimation Method

Abstract. The Lo's R/S tests (Lo, 1991), GPH test (Geweke and Porter-Hudak, 1983) and the maximum likelihood estimation method implemented in S-Plus (S-MLE) are evaluated through intensive Mote Carlo simulations for detecting the existence of long-memory. It is shown that, it is difficult to find an appropriate lag q for Lo's test for different AR and ARFIMA processes, which makes the use of Lo's test very tricky. In general, the GPH test outperforms the Lo's test, but for cases where there is strong autocorrelations (e.g., AR(1) processes with φ=0.97 or even 0.99), the GPH test is totally useless, even for time series of large data size. Although S-MLE method does not provide a statistic test for the existence of long-memory, the estimates of d given by S-MLE seems to give a good indication of whether or not the long-memory is present. Data size has a significant impact on the power of all the three methods. Generally, the power of Lo's test and GPH test increases with the increase of data size, and the estimates of d with GPH test and S-MLE converge with the increase of data size. According to the results with the Lo's R/S test (Lo, 1991), GPH test (Geweke and Porter-Hudak, 1983) and the S-MLE method, all daily flow series exhibit long-memory. The intensity of long-memory in daily streamflow processes has only a very weak positive relationship with the scale of watershed.

Parameter Estimation of Weibull Distribution Model Based on Ant Colony Algorithm

2014 ◽  
Vol 1070-1072 ◽  
pp. 2073-2078
Author(s):  
Xiu Ji ◽  
Hui Wang ◽  
Chuan Qi Zhao ◽  
Xu Ting Yan
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Ant Colony Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Ant Colony ◽  
Likelihood Method ◽  
Distribution Model ◽  
Algorithm Theory

It is difficult to estimate the parameters of Weibull distribution model using maximum likelihood estimation based on particle swarm optimization (PSO) theory for which is easy to fall into premature and needs more variables, ant colony algorithm theory was introduced into maximum likelihood method, and a parameter estimation method based on ant colony algorithm theory was proposed, an example was simulated to verify the feasibility and effectiveness of this method by comparing with ant colony algorithm and PSO.This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

A Monte Carlo Maximum Likelihood Method for Estimating Uncertainty Arising from Shared Errors in Exposures in Epidemiological Studies of Nuclear Workers

2007 ◽  
Vol 168 (6) ◽  
pp. 757-763 ◽  
Author(s):  
Leslie Stayner ◽  
Martine Vrijheid ◽  
Elisabeth Cardis ◽  
Daniel O. Stram ◽  
Isabelle Deltour ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Epidemiological Studies ◽  
Likelihood Method ◽  
Nuclear Workers ◽  
Monte Carlo Maximum Likelihood

scholarly journals مقارنة طرائق تقدير معلمات توزيع كاما ذي المعلمتين في حالة البيانات المفقودة باستخدام المحاكاة

2008 ◽  
Vol 14 (51) ◽  
Author(s):  
ظافر حسين رشيد ◽  
اوات سردار وادي
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Shrinkage Method

المستخلص تم في هذا البحث تقدير معلمات توزيع كاما ذي المعلمتين في حالة البيانات المفقودة وذلك باستخدام اثنين من الطرائق المهمة وهما: طريقة الامكان الأعظم (Maximum Likelihood Method) والتي تضمنت ثلاث طرائق لحل معادلات الإمكان غير الخطية التي يتم الحصول من خلالها على ثلاث مقدرات للإمكان الأعظم وهي: طريقة نيوتن- رافسن وطريقتين تم تطويرهما في هذا البحث لتلائم حالة البيانات المفقودة وهما تطوير طريقة (Thom) وتطوير طريقة (Sinha)، فضلاً عن تطوير طريقة أخرى تعتمد على توزيع كاما ذي المعلمات الثلاث في إيجاد مقدرات الإمكان الأعظم وهي تطوير طريقة (Bowman, Shenton and Lam) وطريقة التقلص (Shrinkage Method). وتم إجراء مقارنة بين أفضلية هذه الطرائق في الجانب التجريبي من خلال أسلوب المحاكاة باستخدام طريقة مونت كارلو (Monte Carlo) وإجراء عدة تجارب مستخدمين المقياس الإحصائي متوسط مربعات الخطأ (MSE) لغرض الحصول على افضل طريقة تقدير.

scholarly journals Parameter estimation in a Black Scholes

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 117-122
Author(s):  
Mustafa Bayram ◽  
Buyukoz Orucova ◽  
Tugcem Partal
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Parametric Method ◽  
Estimation Method ◽  
Parametric Estimation ◽  
Likelihood Method ◽  
Observation Data ◽  
Unknown Parameters ◽  
Black Scholes ◽  
Non Parametric

In this paper we discuss parameter estimation in black scholes model. A non-parametric estimation method and well known maximum likelihood estimator are considered. Our aim is to estimate the unknown parameters for stochastic differential equation with discrete time observation data. In simulation study we compare the non-parametric method with maximum likelihood method using stochastic numerical scheme named with Euler Maruyama.

scholarly journals A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling

2020 ◽  
Vol 8 (2) ◽  
pp. 610-630 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Emrah Altun EA ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Estimation Method ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Survival Times ◽  
New Model ◽  
Von Mises ◽  
Bootstrapping Method

In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the Maximum likelihood method, Cram er-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.

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