scholarly journals Different Estimation Procedures for the Parameters of the Extended Exponential Geometric Distribution for Medical Data

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Francisco Louzada ◽  
Pedro L. Ramos ◽  
Gleici S. C. Perdoná
Keyword(s):  
Geometric Distribution ◽  
Weighted Least Squares ◽  
Likelihood Method ◽  
Data Sets ◽  
Unknown Parameters ◽  
Simple Alternative ◽  
Estimation Procedures ◽  
Minimum Distance Estimators ◽  
Mean Square Errors ◽  
Modified Moments

We have considered different estimation procedures for the unknown parameters of the extended exponential geometric distribution. We introduce different types of estimators such as the maximum likelihood, method of moments, modified moments,L-moments, ordinary and weighted least squares, percentile, maximum product of spacings, and minimum distance estimators. The different estimators are compared by using extensive numerical simulations. We discovered that the maximum product of spacings estimator has the smallest mean square errors and mean relative estimates, nearest to one, for both parameters, proving to be the most efficient method compared to other methods. Combining these results with the good properties of the method such as consistency, asymptotic efficiency, normality, and invariance we conclude that the maximum product of spacings estimator is the best one for estimating the parameters of the extended exponential geometric distribution in comparison with its competitors. For the sake of illustration, we apply our proposed methodology in two important data sets, demonstrating that the EEG distribution is a simple alternative to be used for lifetime data.

Estimating Regression Models in Which the Dependent Variable Is Based on Estimates

2005 ◽  
Vol 13 (4) ◽  
pp. 345-364 ◽  
Author(s):  
Jeffrey B. Lewis ◽  
Drew A. Linzer
Keyword(s):  
Weighted Least Squares ◽  
Standard Errors ◽  
National Study ◽  
Data Sets ◽  
Sampling Variance ◽  
Presidential Approval ◽  
Units Of Analysis ◽  
Simple Alternative ◽  
Dependent Variables ◽  
Cross National Study

Researchers often use as dependent variables quantities estimated from auxiliary data sets. Estimated dependent variable (EDV) models arise, for example, in studies where counties or states are the units of analysis and the dependent variable is an estimated mean, proportion, or regression coefficient. Scholars fitting EDV models have generally recognized that variation in the sampling variance of the observations on the dependent variable will induce heteroscedasticity. We show that the most common approach to this problem, weighted least squares, will usually lead to inefficient estimates and underestimated standard errors. In many cases, OLS with White's or Efron heteroscedastic consistent standard errors yields better results. We also suggest two simple alternative FGLS approaches that are more efficient and yield consistent standard error estimates. Finally, we apply the various alternative estimators to a replication of Cohen's (2004) cross-national study of presidential approval.

scholarly journals Binomial-exponential 2 Distribution: Different Estimation Methods and Weather Applications

2017 ◽  
Vol 18 (2) ◽  
pp. 0233 ◽  
Author(s):  
Hassan S Bakouch ◽  
Sanku Dey ◽  
Pedro Luiz Ramos ◽  
Francisco Louzada
Keyword(s):  
Method Of Moments ◽  
Minimum Distance ◽  
Real Data ◽  
Ordinary Least Squares ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Anderson Darling ◽  
Von Mises ◽  
Modified Moments

In this paper, we have considered different estimation methods of the unknown parameters of a binomial-exponential 2 distribution. First, we briefly describe different frequentist approaches such as the method of moments, modified moments, ordinary least-squares estimation, weightedleast-squares estimation, percentile, maximum product of spacings, Cramer-von Mises type minimum distance, Anderson-Darling and Right-tail Anderson-Darling, and compare them using extensive numerical simulations. We apply our proposed methodology to three real data sets related to the total monthly rainfall during April, May and September at Sao Carlos, Brazil.

Weighted-exponential regression model: An alternative to the gamma regression model

2019 ◽  
Vol 10 (06) ◽  
pp. 1950035 ◽  
Author(s):  
Emrah Altun
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Response Variable ◽  
Exponential Regression ◽  
Exponential Regression Model ◽  
The Right

In this study, weighted-exponential regression model is proposed for modeling the right-skewed response variable as an alternative to the gamma regression model. The maximum likelihood, method of moments, least-squares and weighted least-squares estimation methods are used to estimate unknown parameters of re-parametrized weighted-exponential distribution. The simulation study is conducted to compare the efficiencies of parameter estimation methods. An application on coalition duration dataset is given to demonstrate the usefulness of proposed regression model against the gamma regression model. The residual analysis is performed to evaluate the accuracy of the fitted model. Empirical findings show that the weighted-exponential regression model provides better fits than the gamma regression model and could be a good choice for modeling the right-skewed response variable.

scholarly journals The Poisson Nadarajah-Haghighi Distribution: Different Methods of Estimation

2021 ◽  
Author(s):  
Sajid Ali ◽  
Sanku Dey ◽  
M H Tahir ◽  
Muhammad Mansoor
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Distribution Functions ◽  
Absolute Difference ◽  
Unknown Parameters ◽  
Data Set ◽  
Bayes Estimates ◽  
Least Squares Estimators ◽  
Anderson Darling ◽  
Mean Square Errors

Estimation of parameters of Poisson Nadarajah-Haghighi (PNH) distribution from the frequentist and Bayesian point of view is discussed in this article. To this end, we briefly described ten different frequentist approaches, namely, the maximum likelihood estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, minimum spacing absolute distance estimators, minimum spacing absolute-log distance estimators, Cramér-von Mises estimators, Anderson-Darling estimators and right-tail Anderson-Darling estimators. To assess the performance of different estimators, Monte Carlo simulations are done for small and large samples. The performance of the estimators is compared in terms of their bias, root mean squares error, average absolute difference between the true and estimated distribution functions, and the maximum absolute difference between the true and estimated distribution functions of the estimates using simulated data. For the Bayesian inference of the unknown parameters, we use Metropolis–Hastings (MH) algorithm to calculate the Bayes estimates and the corresponding credible intervals. Results from the simulation study suggests that among the considered classical methods of estimation, weighted least squares and the maximum product spacing estimators uniformly produces the least biases of the estimates with least root mean square errors. However, Bayes estimates perform better than all other estimates. Finally, we discuss a practical data set to show the application of the distribution.

scholarly journals Transmuted Topp-Leone Weibull Lifetime Distribution: Statistical Properties and Different Method of Estimation

2020 ◽  
pp. 501-515 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Haitham Yousof
Keyword(s):  
Carbon Fibers ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Type Model ◽  
Data Sets ◽  
Unknown Parameters ◽  
Renyi’S Entropy ◽  
Von Mises ◽  
Leukemia Data

In this work we focus on proposing a new lifetime Weibull type model called the transmuted Topp-Leone Weibull and studying its properties. We derive some new bivariate and multivariate transmuted Topp-Leone Weibull versions using “Farlie Gumbel Morgenstern (FGM) Copula”, “modified FGM Copula”, “Clayton Copula” and “Renyi's entropy Copula”. The estimation of its unknown parameters is carried out by considering different method of estimation. The statistical performances of all methods are studied by two real data sets and a numerical Monte Carlo simulation. The Cramer-Von Mises method is the best method for modeling the carbon fibers data. The maximum likelihood method is the best method for modeling the Leukemia data, however all other methods performed well.

scholarly journals Bayesian and Classical Estimation for the One Parameter Double Lindley Model

2020 ◽  
pp. 409-420 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Wahhab Mohammed ◽  
Haitham M. Yousof
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Estimation Method ◽  
Ordinary Least Squares ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Weighted Least Squares Method ◽  
Von Mises ◽  
New Distribution

The main motivation of this paper is to show how the different frequentist estimators of the new distribution perform for different sample sizes and different parameter values and to raise a guideline in choosing the best estimation method for the new model. The unknown parameters of the new distribution are estimated using the maximum likelihood method, ordinary least squares method, weighted least squares method, Cramer-Von-Mises method and Bayesian method. The obtained estimators are compared using Markov Chain Monte Carlo simulations and we observed that Bayesian estimators are more efficient compared to other the estimators.

scholarly journals New Method for Generating New Families of Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 726
Author(s):  
Lamya A. Baharith ◽  
Wedad H. Aljuhani
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Rate Function ◽  
New Method ◽  
Likelihood Method ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
New Approach ◽  
Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

scholarly journals The Censored Beta-Skew Alpha-Power Distribution

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1114
Author(s):  
Guillermo Martínez-Flórez ◽  
Roger Tovar-Falón ◽  
María Martínez-Guerra
Keyword(s):  
Power Distribution ◽  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Score Functions ◽  
New Family ◽  
Two Parameters ◽  
Family Of Distributions

This paper introduces a new family of distributions for modelling censored multimodal data. The model extends the widely known tobit model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new family of distributions are studied in detail and a model for censored positive data is also studied. The problem of estimating parameters is addressed by considering the maximum likelihood method. The score functions and the elements of the observed information matrix are given. Finally, three applications to real data sets are reported to illustrate the developed methodology.

scholarly journals Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

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