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.

scholarly journals The Effect of Estimating the Shape Parameter on Probability Distributions Using the Moment Method

2018 ◽  
Vol 2 (3) ◽  
Author(s):  
Hamza Ibrahim Hamza
Keyword(s):  
Shape Parameter ◽  
Probability Distributions ◽  
Estimation Method ◽  
Simulation Method ◽  
Inductive Method ◽  
Binomial Distributions ◽  
Matlab Program ◽  
Best Estimate ◽  
The Mean ◽  
The Moment

  The purpose of this paper was to identify the values ​​of the parameters of the shape of the binomial, Poisson and natural distributions. Using the estimation 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, 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. For estimating the parameter of figure (0.5), (0.7), (0.9) Among distributions. The paper also issued a number of recommendations, most notably the use of binomial distribution to estimate the parameter of the figure (0.9) at the size of sample (10), (30), (50), (70).  

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.

scholarly journals A New Family of Continuous Probability Distributions

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 194
Author(s):  
M. El-Morshedy ◽  
Fahad Sameer Alshammari ◽  
Yasser S. Hamed ◽  
Mohammed S. Eliwa ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Real Life ◽  
Likelihood Method ◽  
Model Parameters ◽  
Finite Sample ◽  
Graphical Simulation ◽  
New Family ◽  
The One

In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of “Farlie-Gumbel-Morgenstern copula”, “the modified Farlie-Gumbel-Morgenstern copula”, “the Clayton copula”, and “the Renyi’s entropy copula” are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to estimate the model parameters. A graphical simulation is performed to assess the finite sample behavior of the estimators of the maximum likelihood method. Two real-life data applications are proposed to illustrate the importance of the new family.

scholarly journals A New Parametric Life Family of Distributions: Properties, Copula and Modeling Failure and Service Times

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1462
Author(s):  
Mansour Shrahili ◽  
Naif Alotaibi
Keyword(s):  
Maximum Likelihood ◽  
Probability Distributions ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
New Family ◽  
Renyi’S Entropy

A new family of probability distributions is defined and applied for modeling symmetric real-life datasets. Some new bivariate type G families using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula and Renyi’s entropy copula are derived. Moreover, some of its statistical properties are presented and studied. Next, the maximum likelihood estimation method is used. A graphical assessment based on biases and mean squared errors is introduced. Based on this assessment, the maximum likelihood method performs well and can be used for estimating the model parameters. Finally, two symmetric real-life applications to illustrate the importance and flexibility of the new family are proposed. The symmetricity of the real data is proved nonparametrically using the kernel density estimation method.

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

Local Intrinsic Dimension Estimation by Generalized Linear Modeling

2017 ◽  
Vol 29 (7) ◽  
pp. 1838-1878 ◽  
Author(s):  
Hideitsu Hino ◽  
Jun Fujiki ◽  
Shotaro Akaho ◽  
Noboru Murata
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Estimation Method ◽  
Likelihood Method ◽  
Local Dimension ◽  
Linear Modeling ◽  
Intrinsic Dimension ◽  
Dimension Estimation ◽  
Generalized Linear Modeling

We propose a method for intrinsic dimension estimation. By fitting the power of distance from an inspection point and the number of samples included inside a ball with a radius equal to the distance, to a regression model, we estimate the goodness of fit. Then, by using the maximum likelihood method, we estimate the local intrinsic dimension around the inspection point. The proposed method is shown to be comparable to conventional methods in global intrinsic dimension estimation experiments. Furthermore, we experimentally show that the proposed method outperforms a conventional local dimension estimation method.

scholarly journals The Odd Power Lindley Generator of Probability Distributions: Properties, Characterizations and Regression Modeling

2019 ◽  
Vol 8 (2) ◽  
pp. 70 ◽  
Author(s):  
Mustafa C. Korkmaz ◽  
Emrah Altun ◽  
Haitham M. Yousof ◽  
G.G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Simulation Studies ◽  
Proposed Model ◽  
Family Of Distributions

In this study, a new flexible family of distributions is proposed with its statistical properties as well as some useful characterizations. The maximum likelihood method is used to estimate the unknown model parameters by means of two simulation studies. A new regression model is proposed based on a special member of the proposed family called, the log odd power Lindley Weibull distribution. Residual analysis is conducted to evaluate the model assumptions. Four applications to real data sets are given to demonstrate the usefulness of the proposed model.

scholarly journals A New Probability Distribution for Modeling Failure and Service Times: Properties, Copulas and Various Estimation Methods

2021 ◽  
Vol 9 (3) ◽  
pp. 555-586
Author(s):  
Hanaa Elgohari ◽  
Mohamed Ibrahim ◽  
Haitham Yousof
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Maximum Likelihood Method ◽  
Estimation Method ◽  
Real Data ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Finite Sample ◽  
Simulation Experiments ◽  
Mean Squared Errors

In this paper, a new generalization of the Pareto type II model is introduced and studied. The new density canbe “right skewed” with heavy tail shape and its corresponding failure rate can be “J-shape”, “decreasing” and “upside down (or increasing-constant-decreasing)”. The new model may be used as an “under-dispersed” and “over-dispersed” model. Bayesian and non-Bayesian estimation methods are considered. We assessed the performance of all methods via simulation study. Bayesian and non-Bayesian estimation methods are compared in modeling real data via two applications. In modeling real data, the maximum likelihood method is the best estimation method. So, we used it in comparing competitive models. Before using the the maximum likelihood method, we performed simulation experiments to assess the finite sample behavior of it using the biases and mean squared errors.

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