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 A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25 ◽  
Author(s):  
Ehab Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Eslam Hafez
Keyword(s):  
Statistical Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Estimation ◽  
Linear Representation ◽  
Rate Function ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Least Squares Estimators ◽  
New Distribution

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

The best least squares approximation problem for a 3-parametric exponential regression model

2000 ◽  
Vol 42 (2) ◽  
pp. 254-266 ◽  
Author(s):  
D. Jukić ◽  
R. Scitovski
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Approximation Problem ◽  
Existence Problem ◽  
Least Squares Approximation ◽  
Exponential Regression ◽  
Exponential Regression Model

AbstractGiven the data (pi, ti, fi), i = 1,…,m, we consider the existence problem for the best least squares approximation of parameters for the 3-parametric exponential regression model. This problem does not always have a solution. In this paper it is shown that this problem has a solution provided that the data are strongly increasing at the ends.

Different inference approaches for the estimators of the sushila distribution

2021 ◽  
Vol 16 (4) ◽  
pp. 251-260
Author(s):  
Marcos Vinicius de Oliveira Peres ◽  
Ricardo Puziol de Oliveira ◽  
Edson Zangiacomi Martinez ◽  
Jorge Alberto Achcar
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Bayesian Method ◽  
Weighted Least Squares ◽  
Computational Cost ◽  
Estimation Method ◽  
Computation Time ◽  
Ordinary Least Squares ◽  
Likelihood Method ◽  
Estimation Methods

In this paper, we order to evaluate via Monte Carlo simulations the performance of sample properties of the estimates of the estimates for Sushila distribution, introduced by Shanker et al. (2013). We consider estimates obtained by six estimation methods, the known approaches of maximum likelihood, moments and Bayesian method, and other less traditional methods: L-moments, ordinary least-squares and weighted least-squares. As a comparison criterion, the biases and the roots of mean-squared errors were used through nine scenarios with samples ranging from 30 to 300 (every 30rd). In addition, we also considered a simulation and a real data application to illustrate the applicability of the proposed estimators as well as the computation time to get the estimates. In this case, the Bayesian method was also considered. The aim of the study was to find an estimation method to be considered as a better alternative or at least interchangeable with the traditional maximum likelihood method considering small or large sample sizes and with low computational cost.

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 Comparisons of six different estimation methods for log-Kumaraswamy distribution

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1839-1847
Author(s):  
Caner Tanis ◽  
Bugra Saracoglu
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Data ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Monte Carlo Simulation Study ◽  
Kumaraswamy Distribution ◽  
Bayesian Least Squares ◽  
Von Mises

In this paper, it is considered the problem of estimation of unknown parameters of log-Kumaraswamy distribution via Monte-Carlo simulations. Firstly, it is described six different estimation methods such as maximum likelihood, approximate bayesian, least-squares, weighted least-squares, percentile, and Cramer-von-Mises. Then, it is performed a Monte-Carlo simulation study to evaluate the performances of these methods according to the biases and mean-squared errors of the estimators. Furthermore, two real data applications based on carbon fibers and the gauge lengths are presented to compare the fits of log-Kumaraswamy and other fitted statistical distributions.

A COMPARISON OF ESTIMATION METHODS FOR ONE PARAMETER INVERSE GOMPERTZ DISTRIBUTION

2021 ◽  
Vol 21 (3) ◽  
pp. 659-668
Author(s):  
CANER TANIŞ ◽  
KADİR KARAKAYA
Keyword(s):  
Least Squares ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Real Data ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Gompertz Distribution ◽  
Weighted Least Squares Method ◽  
Von Mises

In this paper, we compare the methods of estimation for one parameter lifetime distribution, which is a special case of inverse Gompertz distribution. We discuss five different estimation methods such as maximum likelihood method, least-squares method, weighted least-squares method, the method of Anderson-Darling, and the method of Crámer–von Mises. It is evaluated the performances of these estimators via Monte Carlo simulations according to the bias and mean-squared error. Furthermore, two real data applications are performed.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

PARAMETER ESTIMATION ON HURDLE POISSON REGRESSION MODEL WITH CENSORED DATA

2012 ◽  
Vol 57 (1) ◽  
Author(s):  
SEYED EHSAN SAFFAR ◽  
ROBIAH ADNAN ◽  
WILLIAM GREENE
Keyword(s):  
Regression Model ◽  
Count Data ◽  
Poisson Regression ◽  
Goodness Of Fit ◽  
Poisson Model ◽  
Likelihood Method ◽  
Poisson Regression Model ◽  
Response Variable ◽  
The Mean ◽  
Over Dispersion

A Poisson model typically is assumed for count data. In many cases, there are many zeros in the dependent variable and because of these many zeros, the mean and the variance values of the dependent variable are not the same as before. In fact, the variance value of the dependent variable will be much more than the mean value of the dependent variable and this is called over–dispersion. Therefore, Poisson model is not suitable anymore for this kind of data because of too many zeros. Thus, it is suggested to use a hurdle Poisson regression model to overcome over–dispersion problem. Furthermore, the response variable in such cases is censored for some values. In this paper, a censored hurdle Poisson regression model is introduced on count data with many zeros. In this model, we consider a response variable and one or more than one explanatory variables. The estimation of regression parameters using the maximum likelihood method is discussed and the goodness–of–fit for the regression model is examined. We study the effects of right censoring on estimated parameters and their standard errors via an example.

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