The exponentiated power exponential regression model with different regression structures: application in nursing data (original) (raw)

The exponentiated power exponential semiparametric regression model

Communications in Statistics - Simulation and Computation, 2020

We propose a new semiparametric regression model with exponentiated power exponential errors using the B-spline basis for nonlinear effects. We adopt the framework of the generalized additive models for location, scale, and shape to fit this regression model. We obtain the maximum penalized likelihood estimates of the model parameters by considering nonlinear effects. Some global-influence measurements and quantile residuals are also investigated. Various Monte Carlo simulations are performed for inference purposes under different parameter settings, systematic components and sample sizes. The proposals are illustrated by two applications to real data.

Generalized Exponentiated Weibull Linear Model in the Presence of Covariates

International Journal of Statistics and Probability, 2017

A new regression model based on the exponentiated Weibull with the structure distribution and the structure of the generalized linear model, called the generalized exponentiated Weibull linear model (GEWLM), is proposed. The GEWLM is composed by three important structural parts: the random component, characterized by the distribution of the response variable; the systematic component, which includes the explanatory variables in the model by means of a linear structure; and a link function, which connects the systematic and random parts of the model. Explicit expressions for the logarithm of the likelihood function, score vector and observed and expected information matrices are presented. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. To detect influential observations in the new model, we use diagnostic measures based on the local influence and Bayesian case influence diagnostics. Also, we show that the estimates of the GEWLM are robust to deal with the presence of outliers in the data. Additionally, to check whether the model supports its assumptions, to detect atypical observations and to verify the goodness-of-fit of the regression model, we define residuals based on the quantile function, and perform a Monte Carlo simulation study to construct confidence bands from the generated envelopes. We apply the new model to a dataset from the insurance area.

Bayesian reference analysis for exponential power regression models

Journal of Statistical Distributions and Applications, 2014

We develop Bayesian reference analyses for linear regression models when the errors follow an exponential power distribution. Specifically, we obtain explicit expressions for reference priors for all the six possible orderings of the model parameters and show that, associated with these six parameters orderings, there are only two reference priors. Further, we show that both of these reference priors lead to proper posterior distributions. Furthermore, we show that the proposed reference Bayesian analyses compare favorably to an analysis based on a competing noninformative prior. Finally, we illustrate these Bayesian reference analyses for exponential power regression models with applications to two datasets. The first application analyzes per capita spending in public schools in the United States. The second application studies the relationship between sold home videos versus profits at the box office.

The Log-exponentiated-Weibull Regression Models with Cure Rate: Local Influence and Residual Analysis

Journal of Data Science, 2021

In this paper the log-exponentiated-Weibull regression model is modified to allow the possibility that long term survivors are present in the data. The modification leads to a log-exponentiated-Weibull regression model with cure rate, encompassing as special cases the log-exponencial regression and log-Weibull regression models with cure rate typically used to model such data. The models attempt to estimate simultaneously the effects of covariates on the acceleration/deceleration of the timing of a given event and the surviving fraction; that is, the proportion of the population for which the event never occurs. Assuming censored data, we consider a classic analysis and Bayesian analysis for the parameters of the proposed model. The normal curvatures of local influence are derived under various perturbation schemes and two deviance-type residuals are proposed to assess departures from the log-exponentiated-Weibull error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.

New regression model with four regression structures and computational aspects

Communications in Statistics - Simulation and Computation, 2017

A new general class of exponentiated sinh Cauchy regression models for location, scale and shape parameters is introduced and studied. It may be applied to censored data and used more effectively in survival analysis when compared with the usual models. For censored data, we employ a frequentist analysis for the parameters of the proposed model. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. The extended regression model is very useful for the analysis of real data and could give more adequate fits than other special regression models.

Application of a power-exponential function-based model to mortality rates forecasting

Communications in Statistics: Case Studies, Data Analysis and Applications, 2019

There are many models for mortality rates. A well-known problem that complicates modeling of human mortality rates is the "accident hump" occurring in early adulthood. Here, two models of mortality rate based on power-exponential functions are presented and compared to a few other models. The models will be fitted to known data of measured death rates from several different countries using numerical techniques for curve-fitting with the nonlinear least-squares method. The properties of the model with respect to forecasting with the Lee-Carter method will be discussed.

On the Selection of Power Transformation Parameters in Regression Analysis

Artificial Intelligence, 2023

In multiple linear regression, there are several classical methods used to estimate the parameters of power transformation models that are used to transform the response variable. Traditionally, these parameters can be estimated using either Maximum Likelihood Estimation or Bayesian methods in conjunction with the other model parameters. In this chapter, attention has been paid to four indicators of the efficiency and reliability of the regressive modeling, and study the possibility of considering them as decision rules through which the optimal power parameter can be chosen. The indicators are the coefficient of determination and p-value of the general linear F-test statistic. Also, the p-value of Shapiro-Wilk test (SWT) statistic for the residual's normality of the estimated linear regression of the transformed response vector and the estimated nonlinear regression of the original response vector resulting from the back transform of the power Transformation model. Real data were used and a computational algorithm was proposed to estimate the optimal power parameter. The authors concluded that the multiplicity of indicators does not lead to obtaining an optimal single value for the power parameter, but this multiplicity may be useful in fortifying the decision-making ability.

The Exponentiated Power Akash Distribution: Properties, Regression, and Applications to Infant Mortality Rate and COVID-19 Patients' Life Cycle

Annals of Biostatistics and Biometric Applications, 2023

The new three-parameter exponentiated power Akash distribution is introduced, and some of its mathematical properties are addressed. Its parameters are estimated by maximum likelihood. A regression model is constructed based on the logarithm of the proposed distribution. The new regression model is deployed to fit COVID-19 censored data with the age of patients and diabetic index as the regressors. The usefulness of the proposed model is proved using the infant mortality rate for some selected countries in 2021.

Unimodal regression in the two-parameter exponential family with constant or known dispersion parameter

In this paper we discuss statistical methods for curve-estimation under the assumption of unimodality for variables with distributions belonging to the two-parameter exponential family with known or constant dispersion parameter. We suggest a non-parametric method based on monotonicity properties. The method is applied to Swedish data on laboratory verified diagnoses of influenza and data on inflation from an episode of hyperinflation in Bulgaria.