scholarly journals Scale Mixture of Rayleigh Distribution

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1842
Author(s):  
Pilar A. Rivera ◽  
Inmaculada Barranco-Chamorro ◽  
Diego I. Gallardo ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Gamma Distribution ◽  
Simulation Study ◽  
Expectation Maximization ◽  
Rayleigh Distribution ◽  
Independent Random Variables ◽  
Scale Mixture ◽  
New Model ◽  
Lifetime Analysis

In this paper, the scale mixture of Rayleigh (SMR) distribution is introduced. It is proven that this new model, initially defined as the quotient of two independent random variables, can be expressed as a scale mixture of a Rayleigh and a particular Generalized Gamma distribution. Closed expressions are obtained for its pdf, cdf, moments, asymmetry and kurtosis coefficients. Its lifetime analysis, properties and Rényi entropy are studied. Inference based on moments and maximum likelihood (ML) is proposed. An Expectation-Maximization (EM) algorithm is implemented to estimate the parameters via ML. This algorithm is also used in a simulation study, which illustrates the good performance of our proposal. Two real datasets are considered in which it is shown that the SMR model provides a good fit and it is more flexible, especially as for kurtosis, than other competitor models, such as the slashed Rayleigh distribution.

scholarly journals Robust mixture regression based on the skew t distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 45-64 ◽  
Author(s):  
Fatma Zehra Doğru ◽  
Olcay Arslan
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Simulation Study ◽  
Expectation Maximization ◽  
Real Data ◽  
Scale Mixture ◽  
Mixture Regression ◽  
Regression Procedure ◽  
Heavy Tailed ◽  
T Distribution

In this study, we propose a robust mixture regression procedure based on the skew t distribution to model heavy-tailed and/or skewed errors in a mixture regression setting. Using the scale mixture representation of the skew  t distribution, we give an Expectation Maximization (EM) algorithm to compute the maximum likelihood (ML) estimates for the paramaters of interest. The performance of proposed estimators is demonstrated by a simulation study and a real data example.

scholarly journals The Odd Log-Logistic Poisson Inverse Rayleigh Distribution: Statistical Properties and Applications

2020 ◽  
pp. 775-787
Author(s):  
Ibrahim Elbatal
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Statistical Properties ◽  
Data Sets ◽  
New Model ◽  
Fundamental Properties

In this work, a new extension of the Inverse Rayleigh model is proposed and studied. We derive some of its fundamental properties. We assess the performance of the maximum likelihood estimators via a simulation study. The importance of the new model is shown via two applications to real data sets. The new model is better fit than other important competitive models based on two real data sets.

scholarly journals A Power Maxwell Distribution with Heavy Tails and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1116 ◽  
Author(s):  
Francisco A. Segovia ◽  
Yolanda M. Gómez ◽  
Osvaldo Venegas ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Expectation Maximization ◽  
Heavy Tails ◽  
Expectation Maximization Algorithm ◽  
Real Data ◽  
Independent Random Variables ◽  
Maxwell Distribution ◽  
Moments Estimators ◽  
New Distribution

In this paper we introduce a distribution which is an extension of the power Maxwell distribution. This new distribution is constructed based on the quotient of two independent random variables, the distributions of which are the power Maxwell distribution and a function of the uniform distribution (0,1) respectively. Thus the result is a distribution with greater kurtosis than the power Maxwell. We study the general density of this distribution, and some properties, moments, asymmetry and kurtosis coefficients. Maximum likelihood and moments estimators are studied. We also develop the expectation–maximization algorithm to make a simulation study and present two applications to real data.

scholarly journals Estimation of 2- and 3-parameter BURR type XII distribution using EM algorithm

2014 ◽  
Vol 10 (2) ◽  
Author(s):  
Nor Hidayah Ismail ◽  
Zarina Mohd Khalid
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Em Algorithm ◽  
Censored Data ◽  
Simulation Study ◽  
Expectation Maximization ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Gamma Distributions ◽  
Burr Type Xii

The Burr Type XII distribution is one of the systems of continuous distributions and is widely known because the distribution includes the characteristics of various well known distributions such as Weibull and gamma distributions. Maximum likelihood estimation (MLE) has been a common method in estimating model parameters. In this paper, we present an alternative method that is expectation-maximization (EM) algorithm to estimate the two- and three- parameter Burr Type XII distributions in the presence of complete and censored data. Furthermore, simulation study is conducted to compare the efficiency and accuracy of MLE and EM algorithm. We discover that EM estimation is more efficient and accurate than those estimates obtained via MLE approach.________________________________________GRAPHICAL ABSTRACT

scholarly journals Finite mixture of compositional regression with gaussian errors

2018 ◽  
Vol 41 (1) ◽  
pp. 75-86
Author(s):  
Taciana Shimizu ◽  
Francisco Louzada ◽  
Adriano Suzuki
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Regression Model ◽  
Simulation Study ◽  
Regression Models ◽  
Finite Mixture ◽  
Maximum Likelihood Estimates ◽  
The Real ◽  
Compositional Structure ◽  
Volleyball Players

In this paper, we consider to evaluate the efficiency of volleyball players according to the performance of attack, block and serve, but considering the compositional structure of the data related to the fundaments. The finite mixture of regression models better fitted the data in comparison with the usual regression model. The maximum likelihood estimates are obtained via an EM algorithm. A simulation study revels that the estimates are closer to the real values, the estimators are asymptotically unbiased for the parameters. A real Brazilian volleyball dataset related to the efficiency of the players is considered for the analysis.

scholarly journals Estimating the relative proportions of SARS-CoV-2 strains from wastewater samples

2022 ◽  
Author(s):  
Lenore Pipes ◽  
Zihao Chen ◽  
Svetlana Afanaseva ◽  
Rasmus Nielsen
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Expectation Maximization ◽  
Initial Step ◽  
Sequencing Depth ◽  
Maximum Likelihood Estimates ◽  
Reference Database ◽  
Wastewater Samples ◽  
Different Strains

Wastewater surveillance has become essential for monitoring the spread of SARS-CoV-2. The quantification of SARS-CoV-2 RNA in wastewater correlates with the Covid-19 caseload in a community. However, estimating the proportions of different SARS-CoV-2 strains has remained technically difficult. We present a method for estimating the relative proportions of SARS-CoV-2 strains from wastewater samples. The method uses an initial step to remove unlikely strains, imputation of missing nucleotides using the global SARS-CoV-2 phylogeny, and an Expectation-Maximization (EM) algorithm for obtaining maximum likelihood estimates of the proportions of different strains in a sample. Using simulations with a reference database of >3 million SARS-CoV-2 genomes, we show that the estimated proportions accurately reflect the true proportions given sufficiently high sequencing depth and that the phylogenetic imputation is highly accurate and substantially improves the reference database.

scholarly journals Robust Mean Change-Point Detecting through Laplace Linear Regression Using EM Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Fengkai Yang
Keyword(s):  
Linear Regression ◽  
Em Algorithm ◽  
Normal Distribution ◽  
Expectation Maximization ◽  
Change Point ◽  
Estimation Algorithm ◽  
Laplace Distribution ◽  
Point Estimation ◽  
Scale Mixture ◽  
Change Point Estimation

We proposed a robust mean change-point estimation algorithm in linear regression with the assumption that the errors follow the Laplace distribution. By representing the Laplace distribution as an appropriate scale mixture of normal distribution, we developed the expectation maximization (EM) algorithm to estimate the position of mean change-point. We investigated the performance of the algorithm through different simulations, finding that our methods is robust to the distributions of errors and is effective to estimate the position of mean change-point. Finally, we applied our method to the classical Holbert data and detected a change-point.

scholarly journals Slashed Exponentiated Rayleigh Distribution

2015 ◽  
Vol 38 (2) ◽  
pp. 453-466 ◽  
Author(s):  
Hugo S. Salinas ◽  
Yuri A. Iriarte ◽  
Heleno Bolfarine
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Random Variable ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Independent Random Variables ◽  
Parameter Estimates ◽  
Positive Data ◽  
New Distribution

<p>In this paper we introduce a new distribution for modeling positive data with high kurtosis. This distribution can be seen as an extension of the exponentiated Rayleigh distribution. This extension builds on the quotient of two independent random variables, one exponentiated Rayleigh in the numerator and Beta(q,1) in the denominator with q&gt;0. It is called the slashed exponentiated Rayleigh random variable. There is evidence that the distribution of this new variable can be more flexible in terms of modeling the kurtosis regarding the exponentiated Rayleigh distribution. The properties of this distribution are studied and the parameter estimates are calculated using the maximum likelihood method. An application with real data reveals good performance of this new distribution.</p>

A Comparison of Maximum Likelihood Estimations for Normal Mean under Right Censoring

2020 ◽  
Vol 72 (2) ◽  
pp. 122-132
Author(s):  
Junfeng Liu ◽  
Xiaoxia Zhang
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Expectation Maximization ◽  
Asymptotic Variance ◽  
Likelihood Estimation ◽  
Right Censoring ◽  
Log Likelihood ◽  
Framework Approach ◽  
Normal Mean ◽  
Maximum Likelihood Estimations

For efficiently estimating the normal mean ([Formula: see text]) under right censoring (threshold =[Formula: see text], [Formula: see text] is known), we compare two approaches within the maximum likelihood estimation (MLE) framework. Approach I is a hierarchical MLE for which only the empirical censoring probability is utilized. Approach II is the direct MLE for which expectation-maximization (EM) algorithm is applied to all individual observations. We use discrete approximation to explain that the asymptotic variance of Approach II estimate equals the inverse Fisher information calculated from the full log-likelihood. We prove that Approach II gives a uniformly smaller asymptotic variance than Approach I and the variance ratio is a decreasing function of [Formula: see text]. We further prove some supportive results and graphically demonstrate that EM algorithm monotonically converges to the unique MLE.

scholarly journals Hybridization of Expectation-Maximization and K-Means Algorithms for Better Clustering Performance

2016 ◽  
Vol 16 (2) ◽  
pp. 16-34 ◽  
Author(s):  
D. Raja Kishor ◽  
N. B. Venkateswarlu
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Expectation Maximization ◽  
Execution Time ◽  
Maximum Likelihood Estimates ◽  
Fitness Value ◽  
Speed Up ◽  
Purdue University ◽  
Synthetic Datasets

Abstract The present work proposes hybridization of Expectation-Maximization (EM) and K-means techniques as an attempt to speed-up the clustering process. Even though both the K-means and EM techniques look into different areas, K-means can be viewed as an approximate way to obtain maximum likelihood estimates for the means. Along with the proposed algorithm for hybridization, the present work also experiments with the Standard EM algorithm. Six different datasets, three of which synthetic datasets, are used for the experiments. Clustering fitness and Sum of Squared Errors (SSE) are computed for measuring the clustering performance. In all the experiments it is observed that the proposed algorithm for hybridization of EM and K-means techniques is consistently taking less execution time with acceptable Clustering Fitness value and less SSE than the standard EM algorithm. It is also observed that the proposed algorithm is producing better clustering results than the Cluster package of Purdue University.

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