Estimation and application in log-Fréchet regression model using censored data

Abstract

This article introduces a new location-scale regression model based on a log-Fréchet distribution. Maximum likelihood and Jackknife methods are used to estimate the new model parameters for censored data. Martingale and deviance residuals are obtained to check model assumptions, data validity, and detect outliers. Moreover, global influence is used to detect influential observations. Monte Carlo simulation study is provided to compare the performance of the maximum likelihood and jackknife estimators for different sample sizes and censoring percentages. The empirical distribution of the martingale and deviance residuals of the proposed model is examined. A real lifetime heart transplant data is analyzed under the log-Fréchet regression model to illustrate the satisfactory results of the proposed model.

The Odds Exponential-Pareto IV Distribution: Regression Model and Application

“…The following are associated with each patient: : log survival time (days); : censoring indicator (1 = dead, 0 = censoring); : is the age (in years); : is the prior surgery coded as (0 = No, 1 = Yes); and : is the transplant coded as (0 = No, 1 = Yes). This data set was used by [ 38 ], [ 35 ], and [ 36 ] for illustrating the log-odd log-logistic Weibull (LOLLW), log-Fréchet (LF), and log-exponentiated Fréchet (LEF) regression models. The LOEPIV regression model will be compared with the log-Weibull (LW), LEP, LOLLW, LF, and LEF regression models.…”

“…It is also widely used in engineering models where failure is accelerated by voltage, temperature, or other stress factors [ 28 ]. Several studies in the literature applied the log-location-scale regression model based on different distributions, such as the log-modified Weibull [ 29 ], the log-Weibull extended [ 30 ], the log-exponentiated Weibull [ 31 ], the log-Burr XII [ 32 ], the log-beta Weibull [ 33 ], the log-beta log-logistic [ 34 ], the log-Fréchet [ 35 ], the log-Exponentiated Fréchet [ 36 ], and the log-gamma-logistic [ 37 ]. Recent studies used the log-location-scale regression model built from the logarithm odd of the distribution.…”

On Odd Perks-G Class of Distributions: Properties, Regression Model, Discretization, Bayesian and Non-Bayesian Estimation, and Applications

“…, X ik ) is the explanatory variable vector, where k is the number of explanatory variables. For more information about linear locationscale regression models, see, for example, [27][28][29][30][31][32].…”