scholarly journals On Zero-Modified Poisson-Sujatha Distribution to Model Overdispersed Count Data

2018 ◽  
Vol 47 (3) ◽  
pp. 1-19
Author(s):  
Wesley Bertoli Da Silva ◽  
Angélica Maria Tortola Ribeiro ◽  
Katiane Silva Conceição ◽  
Marinho Gomes Andrade ◽  
Francisco Louzada Neto
Keyword(s):  
Biological Sciences ◽  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Simulation Study ◽  
Count Data ◽  
Probability Function ◽  
Hurdle Model ◽  
Asymptotic Inference ◽  
Proposed Model

In this paper we propose the zero-modified Poisson-Sujatha distribution as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros. It will be shown that the zero modification can be incorporated by using the zero-truncated Poisson-Sujatha distribution. A simple reparametrization of the probability function will allow us to represent the zero-modified Poisson-Sujatha distribution as a hurdle model. This trick leads to the fact that proposed model can be fitted without any previously information about the zero modification present in a given dataset. The maximum likelihood theory will be used for parameter estimation and asymptotic inference concerns. A simulation study will be conducted in order to evaluate some frequentist properties of the developed methodology. The usefulness of the proposed model will be illustrated using real datasets of the biological sciences field and comparing it with other models available in the literature.

scholarly journals Comparing of Car-Bym, Generalized Poisson dan Negative Binomial on Tuberculosis Data in Banyumas Districs

2021 ◽  
Vol 5 (1) ◽  
pp. 130-140
Author(s):  
Jajang Jajang ◽  
Budi Pratikno ◽  
Mashuri Mashuri
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Count Data ◽  
Degrees Of Freedom ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Poisson Model ◽  
Generalized Poisson ◽  
Central Java ◽  
Area Data

In 2019 the number of people with TB (Tuberculosis) in Banyumas, Central Java, is high (1,910 people have been detected with TB). The number of people infected Tuberculosis (TB) in Banyumas is the count data and it is also the area data. In modeling, the parameter estimation and characteristic of the data need to be considered. Here, we studied comparing Generalized Poisson (GP), negative binomial (NB), and Poisson and CAR.BYM model for TB cases in Banyumas. Here, we use two methods for parameter estimation, maximum likelihood estimation (MLE) and Bayes. The MLE is used for GP and NB models, whereas Bayes is used for Poisson and CAR-BYM. The results showed that Poisson model detected overdispersion where deviance value is 67.38 for 22 degrees of freedom. Therefore, ratio of deviance to degrees of freedom is 3.06 (>1). This indicates that there was overdispersion. The folowing GP, NB, Poisson-Bayes and CAR-BYM are used to modeling TB data in Banyumas and we compare their RMSE. With refer to RMES criteria, we found that CAR-BYM is the best model for modeling TB in Banyumas because its RMSE is smallest.

scholarly journals Modified Slash Lindley Distribution

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jimmy Reyes ◽  
Osvaldo Venegas ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Lindley Distribution ◽  
Basic Properties ◽  
Moment Estimators ◽  
Proposed Model ◽  
Distribution Moment ◽  
Flexible Models ◽  
New Distribution

In this paper we introduce a new distribution, called the modified slash Lindley distribution, which can be seen as an extension of the Lindley distribution. We show that this new distribution provides more flexibility in terms of kurtosis and skewness than the Lindley distribution. We derive moments and some basic properties for the new distribution. Moment estimators and maximum likelihood estimators are calculated using numerical procedures. We carry out a simulation study for the maximum likelihood estimators. A fit of the proposed model indicates good performance when compared with other less flexible models.

Zero-Inflated Poisson Model with Group Data

2012 ◽  
Vol 569 ◽  
pp. 627-631
Author(s):  
Jun Yang ◽  
Xin Zhang
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Model Selection ◽  
Count Data ◽  
Maximum Likelihood Estimate ◽  
Poisson Model ◽  
Cigarette Consumption ◽  
Chi Square ◽  
Group Data ◽  
Chi Square Test

The Zero-inflated Poisson model has been widely used in many fields for count data with excessive zeroes. In fact, group data are often collected for many count data, such as cigarette consumption. In order to solve the problem, Zero-inflated Poisson model with group data is investigated in this paper. Parameter estimation is given by the maximum likelihood estimate, model selection is discussed by the Chi-square test, and one real example is given for application in the end.

scholarly journals Estimation a Stress-Strength Model for P (Yr:n1 < Xk:n2 ) Using the Lindley Distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 105-121 ◽  
Author(s):  
Marwa Khalil
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Real Data ◽  
Minimum Variance ◽  
Strength Model ◽  
Practical Application ◽  
Likelihood Estimator ◽  
Lindley Distribution ◽  
Minimum Variance Unbiased Estimator ◽  
Proposed Model

The problem of estimation reliability in a multicomponent stress-strength model, when the system consists of k components have strength each compo- nent experiencing a random stress, is considered in this paper. The reliability of such a system is obtained when strength and stress variables are given by Lindley distribution. The system is regarded as alive only if at least r out of k (r < k) strength exceeds the stress. The multicomponent reliability of the system is given by Rr,k . The maximum likelihood estimator (M LE), uniformly minimum variance unbiased estimator (UMVUE) and Bayes esti- mator of Rr,k are obtained. A simulation study is performed to compare the different estimators of Rr,k . Real data is used as a practical application of the proposed model.

Inference on Parameters of a Geometric Process with Scaled Muth Distribution

2020 ◽  
pp. 2150006
Author(s):  
Cenker Biçer ◽  
Hassan S. Bakouch ◽  
Hayrinisa Demirci Biçer
Keyword(s):  
Maximum Likelihood ◽  
Process Parameters ◽  
Simulation Study ◽  
Count Data ◽  
Probability Model ◽  
Renewal Processes ◽  
Occurrence Time ◽  
Geometric Process ◽  
First Occurrence ◽  
Gp Model

The problem of statistical modeling of the geometric count data with a specific probability model of lifetimes is of interest and importance in reliability. In this paper, we construct a geometric process (GP), with parameter [Formula: see text], for modeling the geometric count data when the distribution of first occurrence time is a scaled Muth with parameters [Formula: see text] and [Formula: see text]. We investigate the estimators of the process parameters [Formula: see text], [Formula: see text] and [Formula: see text] from a point of approximations of classical and modified approach by using the different estimation methodologies such as the maximum likelihood, moments, least-squares and maximum spacing. We perform a simulation study to compare the estimation performance of the estimators obtained. Finally, we provide an illustrative analysis conducted on a real-world dataset to show the efficiency of the GP model constructed in this paper against the alpha-series and renewal processes and exemplify the data modeling stages. Consequently, a forecasting to such data using the GP with the scaled Muth is investigated.

scholarly journals REGRESI POISSON BIVARIAT DENGAN KOVARIAN MERUPAKAN FUNGSI DARI VARIABEL BEBAS

2018 ◽  
Vol 2 (1) ◽  
pp. 23-34
Author(s):  
Untung Kurniawan
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Infant Mortality ◽  
Maternal Mortality ◽  
Regression Model ◽  
Pregnant Women ◽  
Significant Influence ◽  
Count Data ◽  
Poisson Regression ◽  
Test Method

Poisson regression is a regression model which often used to analyze the count data. In this study, poisson regression has been used bivariate poisson regression where the regression is a method which is used to model a pair of correlated count data with multiple predictor variables. The model is used covariance which has a function of the independent variable. The purposes of this study is obtain parameter estimates, test statistics of bivariate poisson regression, and determine the factors that influence of infant mortality and maternal mortality. The data is used from the infant mortality and maternal mortality in Central Java 2015. Based on the result, the parameter estimation of poisson bivariate regression model using maximum likelihood (MLE) method. The results obtained from the parameter estimation are not close form so it needs to be done by Newton-Raphson iteration method. In testing the hypothesis using the Maximum Likelihood Ratio Test method (MLRT) by comparing the value between likelihood below H0 and likelihood below population. Partial of parameters model λ1 (infant mortality) there are six independent variables that have significant influence, namely, delivery by health personnel (X1), pregnant women carry out the program K4 (X3), pregnant women who get Fe3 tablet (X4), handling obstetric complication (X5), exclusively breastfed infants (X7), and households living a clean and healthy life (X8). While for model λ2 (maternal death) only variable handling of neonatal complication (X6) which have no significant influence to response variable.

scholarly journals The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248873
Author(s):  
Majdah Badr ◽  
Muhammad Ijaz
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Probability Distribution ◽  
Simulation Study ◽  
Probability Distributions ◽  
Simulated Data ◽  
Maximum Likelihood Estimators ◽  
Data Sets ◽  
Lifetime Data ◽  
Confidence Bounds

The paper addresses a new four-parameter probability distribution called the Exponentiated Exponential Burr XII or abbreviated as EE-BXII. We derive various statistical properties in addition to the parameter estimation, moments, and asymptotic confidence bounds. We estimate the precision of the maximum likelihood estimators via a simulation study. Furthermore, the utility of the proposed distribution is evaluated by using two lifetime data sets and the results are compared with other existing probability distributions. The results clarify that the proposed distribution provides a better fit to these data sets as compared to the existing probability distributions.

scholarly journals Weighted stochastic block model

2021 ◽  
Author(s):  
Tin Lok James Ng ◽  
Thomas Brendan Murphy
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Simulated Data ◽  
Important Case ◽  
Block Model ◽  
Data Set ◽  
Stochastic Block Model ◽  
Proposed Model ◽  
Variational Approaches ◽  
Number Of Classes

AbstractWe propose a weighted stochastic block model (WSBM) which extends the stochastic block model to the important case in which edges are weighted. We address the parameter estimation of the WSBM by use of maximum likelihood and variational approaches, and establish the consistency of these estimators. The problem of choosing the number of classes in a WSBM is addressed. The proposed model is applied to simulated data and an illustrative data set.

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