On the Usefulness of the Logarithmic Skew Normal Distribution for Describing Claims Size Data

In this paper, the three-parameter skew lognormal distribution is proposed to model actuarial data concerning losses. This distribution yields a satisfactory fit to empirical data in the whole range of the empirical distribution as compared to other distributions used in the actuarial statistics literature. To the best of our knowledge, this distribution has not been used in insurance context and it might be suitable for computing reinsurance premiums in situations where the right tail of the empirical distribution plays an important role. Furthermore, a regression model can be simply derived to explain the response variable as a function of a set of explanatory variables.

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The Odd Log-Logistic Geometric Normal Regression Model with Applications

Advances in Data Science and Adaptive Analysis ◽

10.1142/s2424922x19500037 ◽

2019 ◽

Vol 11 (01n02) ◽

pp. 1950003

Author(s):

Fábio Prataviera ◽

Gauss M. Cordeiro ◽

Edwin M. M. Ortega ◽

Adriano K. Suzuki

Keyword(s):

Regression Model ◽

Normal Distribution ◽

Regression Models ◽

Empirical Distribution ◽

Real Data ◽

Likelihood Method ◽

Standard Normal Distribution ◽

Model Parameters ◽

Diagnostic Measures ◽

Standard Normal

In several applications, the distribution of the data is frequently unimodal, asymmetric or bimodal. The regression models commonly used for applications to data with real support are the normal, skew normal, beta normal and gamma normal, among others. We define a new regression model based on the odd log-logistic geometric normal distribution for modeling asymmetric or bimodal data with support in [Formula: see text], which generalizes some known regression models including the widely known heteroscedastic linear regression. We adopt the maximum likelihood method for estimating the model parameters and define diagnostic measures to detect influential observations. For some parameter settings, sample sizes and different systematic structures, various simulations are performed to verify the adequacy of the estimators of the model parameters. The empirical distribution of the quantile residuals is investigated and compared with the standard normal distribution. We prove empirically the usefulness of the proposed models by means of three applications to real data.

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A New Ridge-Type Estimator for the Gamma Regression Model

Scientifica ◽

10.1155/2021/5545356 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Adewale F. Lukman ◽

Issam Dawoud ◽

B. M. Golam Kibria ◽

Zakariya Y. Algamal ◽

Benedicta Aladeitan

Keyword(s):

Biological Activity ◽

Regression Model ◽

Mean Squared Error ◽

Real Life ◽

Regression Parameter ◽

Likelihood Estimator ◽

Response Variable ◽

Explanatory Variables ◽

Squared Error ◽

The Mean

The known linear regression model (LRM) is used mostly for modelling the QSAR relationship between the response variable (biological activity) and one or more physiochemical or structural properties which serve as the explanatory variables mainly when the distribution of the response variable is normal. The gamma regression model is employed often for a skewed dependent variable. The parameters in both models are estimated using the maximum likelihood estimator (MLE). However, the MLE becomes unstable in the presence of multicollinearity for both models. In this study, we propose a new estimator and suggest some biasing parameters to estimate the regression parameter for the gamma regression model when there is multicollinearity. A simulation study and a real-life application were performed for evaluating the estimators' performance via the mean squared error criterion. The results from simulation and the real-life application revealed that the proposed gamma estimator produced lower MSE values than other considered estimators.

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The Factors Affecting Eye Patients (Cataract) In Jordan by Using the Logistic Regression Model

Modern Applied Science ◽

10.5539/mas.v11n8p38 ◽

2017 ◽

Vol 11 (8) ◽

pp. 38

Author(s):

Adeeb Ahmed Ali AL Rahamneh ◽

Omar M. Hawamdeh

Keyword(s):

Logistic Regression ◽

Regression Model ◽

Likelihood Ratio Test ◽

Logistic Regression Model ◽

Ratio Test ◽

Response Variable ◽

Factors Affecting ◽

Independent Variables ◽

Lemeshow Test ◽

The Right

This study aims to use the logistic regression model to classify patients as infected and without cataracts. The independent variables were used to represent the gender, the age, the pressure in the right eye, the pressure in the left eye, HbA1C, and the anemia, representative variables for the study of Cataract disease affects the eyes, based on a random sample of (116) patients. The results proved that the used logistic regression model is an efficient and representative for data that shows through (Likelihood Ratio Test) and (Hosmer and Lemeshow test), and the study proved that the value of (R Square Nagelkerke=1) this means that 100% of the change in the occurred changes in the response variable explained through the Logistic regression model.

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

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s1793962319500351 ◽

2019 ◽

Vol 10 (06) ◽

pp. 1950035 ◽

Cited By ~ 1

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.

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Profile Monitoring for Com Poisson Responses

Journal of University of Shanghai for Science and Technology ◽

10.51201/jusst12578 ◽

2021 ◽

Vol 23 (1) ◽

Author(s):

El-Housainy A.Rady ◽

◽

Hadel Z. Ahmed ◽

Mohamed S.M. ◽

Keyword(s):

Phase I ◽

Normal Distribution ◽

Parametric Estimation ◽

Quality Characteristic ◽

Profile Monitoring ◽

Response Variable ◽

Explanatory Variables ◽

Response Profiles ◽

The Relationship ◽

Over Time

In some real case problems, the relationship between a response variable and one or more explanatory variables called as profile should be monitored over time instead of the quality characteristic itself. Profile monitoring is used in such instances. Many researches have been done in the area of profile monitoring but in most of them it is assumed that the response variable follows normal distribution. In recent years Yeh et al. (2009) proposed 5 T2 based methods for monitoring logistic profiles in which response variable is binary and Amiri et al. (2011) evaluate two of the best T2 methods for Poisson response profiles monitoring in Phase I. In this paper we will obtain the form of the Com Poisson equation and parametric estimation.

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Analysis of covariance by assuming a skew normal distribution for response variable

Hacettepe Journal of Mathematics and Statistics ◽

10.15672/hjms.20159314058 ◽

2015 ◽

Vol 46 (94) ◽

pp. 1-1

Author(s):

Afshin Fallah ◽

Zahra Goodarzi

Keyword(s):

Normal Distribution ◽

Analysis Of Covariance ◽

Skew Normal Distribution ◽

Response Variable ◽

Skew Normal

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Modeling Proportion Data with Inflation by Using a Power-Skew-Normal/Logit Mixture Model

Mathematics ◽

10.3390/math9161989 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1989

Author(s):

Guillermo Martínez-Flórez ◽

Hector W. Gomez ◽

Roger Tovar-Falón

Keyword(s):

Regression Model ◽

Logistic Model ◽

Information Matrix ◽

Link Function ◽

Skew Normal Distribution ◽

Linear Predictor ◽

Response Variable ◽

Proposed Model ◽

Flexible Model ◽

Skew Normal

Rate or proportion data are modeled by using a regression model. The considered regression model can be used for studying phenomena with a response on the (0, 1), [0, 1), (0, 1], or [0, 1] intervals. To connect the response variable with the linear predictor in the regression model, we use a logit link function, which guarantees that the obtained prediction ranges between zero and one in the cases inflated at zero or one (or both). The model is complemented with the assumption that the errors follow a power-skew-normal distribution, resulting in a very flexible model, and with a non-singular information matrix, constituting an advantage over other existing models in the literature. To explain the probability of point mass at the values zero and/or one (inflated part), we used a polytomic logistic model with covariates. The results of two illustrations showed that the proposed model is a better alternative compared to widely known models in the literature.

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