scholarly journals Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2164
Author(s):  
Héctor J. Gómez ◽  
Diego I. Gallardo ◽  
Karol I. Santoro
Keyword(s):  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
R Software ◽  
Data Application ◽  
The Em Algorithm ◽  
Kurtosis Parameter ◽  
Computational Implementation ◽  
Moments Method

In this paper, we present an extension of the truncated positive normal (TPN) distribution to model positive data with a high kurtosis. The new model is defined as the quotient between two random variables: the TPN distribution (numerator) and the power of a standard uniform distribution (denominator). The resulting model has greater kurtosis than the TPN distribution. We studied some properties of the distribution, such as moments, asymmetry, and kurtosis. Parameter estimation is based on the moments method, and maximum likelihood estimation uses the expectation-maximization algorithm. We performed some simulation studies to assess the recovery parameters and illustrate the model with a real data application related to body weight. The computational implementation of this work was included in the tpn package of the R software.

EFFICIENT ESTIMATION OF ERLANG MIXTURES USING iSCAD PENALTY WITH INSURANCE APPLICATION

2016 ◽  
Vol 46 (3) ◽  
pp. 779-799 ◽  
Author(s):  
Cuihong Yin ◽  
X. Sheldon Lin
Keyword(s):  
Em Algorithm ◽  
Mixture Model ◽  
Penalty Function ◽  
Real Data ◽  
Efficient Estimation ◽  
Model Parameters ◽  
Simulation Studies ◽  
Distributional Properties ◽  
Data Application ◽  
The Em Algorithm

AbstractThe Erlang mixture model has been widely used in modeling insurance losses due to its desirable distributional properties. In this paper, we consider the problem of efficient estimation of the Erlang mixture model. We present a new thresholding penalty function and a corresponding EM algorithm to estimate model parameters and to determine the order of the mixture. Using simulation studies and a real data application, we demonstrate the efficiency of the EM algorithm.

scholarly journals Mixture of Lindley and Inverse Weibull Distributions: Properties and Estimation

2021 ◽  
Vol 20 ◽  
pp. 134-143
Author(s):  
A. S. Al-Moisheer ◽  
A. F. Daghestani ◽  
K. S. Sultan
Keyword(s):  
Method Of Moments ◽  
Generalized Method Of Moments ◽  
Real Data ◽  
Estimation Methods ◽  
Simulation Studies ◽  
Weibull Distributions ◽  
Unknown Parameters ◽  
Data Application ◽  
Rate Functions ◽  
And Behavior

In this paper, we talk about a mixture of one-parameter Lindley and inverse Weibull distributions (MLIWD). First, We introduce and discuss the MLIWD. Then, we study the main statistical properties of the proposed mixture and provide some graphs of both the density and the associated hazard rate functions. After that, we estimate the unknown parameters of the proposed mixture via two estimation methods, namely, the generalized method of moments and maximum likelihood. In addition, we compare the estimation methods via some simulation studies to determine the efficacy of the two estimation methods. Finally, we evaluate the performance and behavior of the proposed mixture with different numerical examples and real data application in survival analysis.

scholarly journals The Exponentiated Lindley Geometric Distribution with Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 510
Author(s):  
Bo Peng ◽  
Zhengqiu Xu ◽  
Min Wang
Keyword(s):  
Maximum Likelihood ◽  
Geometric Distribution ◽  
Residual Life ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters

We introduce a new three-parameter lifetime distribution, the exponentiated Lindley geometric distribution, which exhibits increasing, decreasing, unimodal, and bathtub shaped hazard rates. We provide statistical properties of the new distribution, including shape of the probability density function, hazard rate function, quantile function, order statistics, moments, residual life function, mean deviations, Bonferroni and Lorenz curves, and entropies. We use maximum likelihood estimation of the unknown parameters, and an Expectation-Maximization algorithm is also developed to find the maximum likelihood estimates. The Fisher information matrix is provided to construct the asymptotic confidence intervals. Finally, two real-data examples are analyzed for illustrative purposes.

Topp–Leone Linear Exponential Distribution

2018 ◽  
Vol 33 (1) ◽  
pp. 31-43
Author(s):  
Bol A. M. Atem ◽  
Suleman Nasiru ◽  
Kwara Nantomah
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Finite Sample ◽  
Data Set ◽  
Finite Sample Properties ◽  
Linear Exponential Distribution

Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

scholarly journals A Multivalent Pairing Model of Linkage Analysis in Autotetraploids

Genetics ◽  
2001 ◽  
Vol 159 (3) ◽  
pp. 1339-1350 ◽  
Author(s):  
Samuel S Wu ◽  
Rongling Wu ◽  
Chang-Xing Ma ◽  
Zhao-Bang Zeng ◽  
Mark C K Yang ◽  
...  
Keyword(s):  
Linkage Analysis ◽  
Linkage Mapping ◽  
Genome Structure ◽  
Likelihood Estimation ◽  
Simulation Studies ◽  
Polyploid Species ◽  
Homologous Chromosomes ◽  
Evolutionary Diversification ◽  
The Em Algorithm ◽  
Pairing Model

Abstract Polyploidy has been recognized as an important step in the evolutionary diversification of flowering plants and may have a significant impact on plant breeding. Statistical analyses for linkage mapping in polyploid species can be difficult due to considerable complexities in polysomic inheritance. In this article, we develop a novel statistical method for linkage analysis of polymorphic markers in a full-sib family of autotetraploids. This method is established on multivalent pairings of homologous chromosomes at meiosis and can provide a simultaneous maximum-likelihood estimation of the double reduction frequencies of and recombination fraction between two markers. The EM algorithm is implemented to provide a tractable way for estimating relative proportions of different modes of gamete formation that generate identical gamete genotypes due to multivalent pairings. Extensive simulation studies were performed to demonstrate the statistical properties of this method. The implications of the new method for understanding the genome structure and organization of polyploid species are discussed.

scholarly journals Insurance ratemaking using the Exponential-Lognormal regression model

2019 ◽  
Vol 14 (1) ◽  
pp. 42-71
Author(s):  
George Tzougas ◽  
Woo Hee Yik ◽  
Muhammad Waqar Mustaqeem
Keyword(s):  
Regression Model ◽  
Negative Binomial ◽  
A Priori ◽  
Likelihood Estimation ◽  
Real Data ◽  
Inverse Gamma ◽  
Data Application ◽  
Expectation Maximisation ◽  
Wide Range ◽  
Gaussian Regression

AbstractThis paper is concerned with presenting the Exponential-Lognormal (ELN) regression model as a competitive alternative to the Pareto, or Exponential-Inverse Gamma, regression model that has been used in a wide range of areas, including insurance ratemaking. This is the first time that the ELN regression model is used in a statistical or actuarial context. The main contribution of the study is that we illustrate how maximum likelihood estimation of the ELN regression model, which does not have a density in closed form, can be accomplished relatively easily via an Expectation-Maximisation type algorithm. A real data application based on motor insurance data is examined in order to emphasise the versatility of the proposed algorithm. Finally, assuming that the number of claims is distributed according to the classic Negative Binomial and Poisson-Inverse Gaussian regression models, both the a priori and a posteriori, or Bonus–Malus, premium rates resulting from the ELN regression model are calculated via the net premium principle and compared to those determined by the Pareto regression model that has been traditionally used for modelling claim sizes.

scholarly journals Bivariate Transmuted Burr Distribution: Properties and Application

2021 ◽  
pp. 15-24
Author(s):  
Muhammad Qaiser Shahbaz ◽  
Jumanah Ahmed Darwish ◽  
Lutfiah Ismail Al Turk
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Bivariate Distribution ◽  
Conditional Distributions ◽  
Conditional Moments ◽  
Data Application ◽  
Burr Distribution ◽  
Rate Functions ◽  
Simultaneous Modeling ◽  
Complex Joint

The bivariate distributions are useful in simultaneous modeling of two random variables. These distributions provide a way of modeling complex joint phenomenon. In this article, a new bivariate distribution is proposed which is known as the bivariate transmuted Burr (BTB) distribution. This new bivariate distribution is extension of the univariate transmuted Burr (TB) distribution to two variables. The proposed  BTB distribution is explored in detail and the marginal and conditional distributions for the distribution are obtained. Joint and conditional moments alongside hazard rate functions are obtained. The maximum likelihood estimation (MLE) for the parameters of the BTB distribution is also done. Finally, real data application of the BTB distribution is given. It is observed that the proposed BTB distribution is a suitable fit for the data used.

scholarly journals A Novel Graphical Evaluation of Agreement

2020 ◽  
Author(s):  
Jongphil Kim ◽  
Ji-Hyun Lee
Keyword(s):  
Correlation Coefficient ◽  
Evaluation Method ◽  
Real Data ◽  
Concordance Correlation Coefficient ◽  
Simulation Studies ◽  
Concordance Correlation ◽  
Data Application ◽  
Study Results ◽  
The Common ◽  
Test Retest Reliability

Abstract Background: The Bland-Altman plot with limit of agreement has been widely used as a visual tool for assessing test-retest reliability or reproducibility between two measurements. We have observed, however, that in certain circumstances the limit of agreement approach may mislead practitioners. Particularly, if the acceptable difference is not available and two readers are highly concordant but the common variance of the data is large, the broad width of the limit of agreement plot may incorrectly indicate a lack of agreement. Methods: This paper proposes a novel, scaled index-based guidance for graphical evaluation of reproducibility or reliability. We create a reference band from two measurements, which is based on the concordance correlation coefficient.Results: Simulation studies have been carried out to demonstrate the benefits of our method over the limit of agreement. We also consider the application to the real examples, including the peak expiratory flow rate data in Bland and Altman's paper and the test-retest reproducibility data of Radiomics study.Conclusions: In absence of acceptable difference, we found that the limit of agreement seems to derive subjective inference and may not be consistent with concordance correlation coefficient. Our simulation study results and real data application show that the proposed method can provide practitioners with a novel graphical evaluation method which is consistent with results from concordance correlation coefficient approach than the limit of agreement approach.

scholarly journals Generalizations of Burr Type X Distribution with Applications

2020 ◽  
pp. 1-8
Author(s):  
Noor Akma Ibrahim ◽  
Mundher Abdullah Khaleel
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Density Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Data Sets ◽  
Lifetime Data ◽  
Simulation Studies ◽  
Cumulative Density Function ◽  
Two Parameters

We propose the generalizations of Burr Type X distribution with two parameters by using the methods of Beta-G, Gamma-G and Weibull-G families of distributions. We discuss maximum likelihood estimation of the model’s parameters. The performances of the parameter’s estimates are assessed via simulation studies under different sets of conditions. In the applications to real data sets, three sets of data are used whereby from the results we can deduce that these models can be used quite effectively in analysing lifetime data. Keywords: cumulative density function; lifetime data; maximum likelihood estimation

scholarly journals Effective estimation algorithm for parameters of multivariate Farlie–Gumbel–Morgenstern copula

2021 ◽  
Author(s):  
Shuhei Ota ◽  
Mitsuhiro Kimura
Keyword(s):  
Parameter Estimation ◽  
Data Analysis ◽  
Computational Complexity ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Asymptotic Normality ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Algorithm ◽  
Simulation Studies

AbstractThis paper focuses on the parameter estimation for the d-variate Farlie–Gumbel–Morgenstern (FGM) copula ($$d\ge 2$$ d ≥ 2 ), which has $$2^d-d-1$$ 2 d - d - 1 dependence parameters to be estimated; therefore, maximum likelihood estimation is not practical for a large d from the viewpoint of computational complexity. Besides, the restriction for the FGM copula’s parameters becomes increasingly complex as d becomes large, which makes parameter estimation difficult. We propose an effective estimation algorithm for the d-variate FGM copula by using the method of inference functions for margins under the restriction of the parameters. We then discuss its asymptotic normality as well as its performance determined through simulation studies. The proposed method is also applied to real data analysis of bearing reliability.

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