Parametric survival models are essential for analyzing time-to-event data in fields such as engineering and biomedicine.While the log-logistic distribution is popular for its simplicity and closed-form expressions,it ...Parametric survival models are essential for analyzing time-to-event data in fields such as engineering and biomedicine.While the log-logistic distribution is popular for its simplicity and closed-form expressions,it often lacks the flexibility needed to capture complex hazard patterns.In this article,we propose a novel extension of the classical log-logistic distribution,termed the new exponential log-logistic(NExLL)distribution,designed to provide enhanced flexibility in modeling time-to-event data with complex failure behaviors.The NExLL model incorporates a new exponential generator to expand the shape adaptability of the baseline log-logistic distribution,allowing it to capture a wide range of hazard rate shapes,including increasing,decreasing,J-shaped,reversed J-shaped,modified bathtub,and unimodal forms.A key feature of the NExLL distribution is its formulation as a mixture of log-logistic densities,offering both symmetric and asymmetric patterns suitable for diverse real-world reliability scenarios.We establish several theoretical properties of the model,including closed-form expressions for its probability density function,cumulative distribution function,moments,hazard rate function,and quantiles.Parameter estimation is performed using seven classical estimation techniques,with extensive Monte Carlo simulations used to evaluate and compare their performance under various conditions.The practical utility and flexibility of the proposed model are illustrated using two real-world datasets from reliability and engineering applications,where the NExLL model demonstrates superior fit and predictive performance compared to existing log-logistic-basedmodels.This contribution advances the toolbox of parametric survivalmodels,offering a robust alternative formodeling complex aging and failure patterns in reliability,engineering,and other applied domains.展开更多
Clustered survival data are widely observed in a variety of setting. Most survival models incorporate clustering and grouping of data accounting for between-cluster variability that creates correlation in order to pre...Clustered survival data are widely observed in a variety of setting. Most survival models incorporate clustering and grouping of data accounting for between-cluster variability that creates correlation in order to prevent underestimate of the standard errors of the parameter estimators but do not include random effects. In this study, we developed a mixed-effect parametric proportional hazard (MEPPH) model with a generalized log-logistic distribution baseline. The parameters of the model were estimated by the application of the maximum likelihood estimation technique with an iterative optimization procedure (quasi-Newton Raphson). The developed MEPPH model’s performance was evaluated using Monte Carlo simulation. The Leukemia dataset with right-censored data was used to demonstrate the model’s applicability. The results revealed that all covariates, except age in PH models, were significant in all considered distributions. Age and Townsend score were significant when the GLL distribution was used in MEPPH, while sex, age and Townsend score were significant in MEPPH model when other distributions were used. Based on information criteria values, the Generalized Log-Logistic Mixed-Effects Parametric Proportional Hazard model (GLL-MEPPH) outperformed other models.展开更多
We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We o...We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We obtain explicit expressions for themoments,moment-generating function,asymptotic distribution,quantile function,mean deviations and distribution of order statistics.The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study.The applicability of the new model is illustrated by means of a real data set.展开更多
In this paper,we studied a two-parameter transmuted model of Log-logistic distribution(LLD)using the quadratic rank transmutation map technique studied by Shaw and Buckley1 as a new survival model in medical sciences ...In this paper,we studied a two-parameter transmuted model of Log-logistic distribution(LLD)using the quadratic rank transmutation map technique studied by Shaw and Buckley1 as a new survival model in medical sciences and other applied fields.Statistical properties of Transmuted LLD(TLLD)are discussed comprehensively.Robust measures of skewness and kurtosis of the proposed model have also been discussed along with graphical overview.The estimation of the model parameters is performed by Maximum Likelihood(ML)method followed by a Monte Carlo(MC)simulation procedure to investigate the performance of the ML estimators and the asymptotic confidence intervals of the parameters.Applications of the proposed model to real-life data are also presented.展开更多
Home mortgage loan lending firms are exposed to many business risks.This paper focuses on the mortgage loan borrower risks and proposes a prospective loss analysis approach in regard to loan repayment defaults of borr...Home mortgage loan lending firms are exposed to many business risks.This paper focuses on the mortgage loan borrower risks and proposes a prospective loss analysis approach in regard to loan repayment defaults of borrowers.For this purpose,a predictive modeling is presented in three stages.In the first stage,occurrence of borrower defaults in a mortgage loans portfolio is modeled through the generalized linear models(GLMs)type regressions for which we specify a logistic distribution for default events.The second stage of modeling develops a survival analysis in order to estimate survival probability and hazard rate functions for individual loans.Ultimately,an expectable loss amount model is presented in the third stage as a function of conditional survival probabilities and corresponding hazard rates at loan levels.Throughout all modeling stages,a large and real data set is used as an empirical analysis case by which detailed interpretations and practical implications of the obtained results are stated.展开更多
We estimate the distribution of COVID-19 mortality(measured as daily deaths)from the start of the pandemic until July 31st,2022,for six European countries and the USA.We use the Pareto,the stretched exponential,the lo...We estimate the distribution of COVID-19 mortality(measured as daily deaths)from the start of the pandemic until July 31st,2022,for six European countries and the USA.We use the Pareto,the stretched exponential,the log-normal and the log-logistic distributions as well as mixtures of the log-normal and log-logistic distributions.The main results are that the Pareto does not describe well the data and that mixture distributions tend to offer a very good fit to the data.We also compute Value-at-Risk measures as well as mortality probabilities with our estimates.We also discuss the implications of our results and findings from the point of view of public health planning and modelling.展开更多
文摘Parametric survival models are essential for analyzing time-to-event data in fields such as engineering and biomedicine.While the log-logistic distribution is popular for its simplicity and closed-form expressions,it often lacks the flexibility needed to capture complex hazard patterns.In this article,we propose a novel extension of the classical log-logistic distribution,termed the new exponential log-logistic(NExLL)distribution,designed to provide enhanced flexibility in modeling time-to-event data with complex failure behaviors.The NExLL model incorporates a new exponential generator to expand the shape adaptability of the baseline log-logistic distribution,allowing it to capture a wide range of hazard rate shapes,including increasing,decreasing,J-shaped,reversed J-shaped,modified bathtub,and unimodal forms.A key feature of the NExLL distribution is its formulation as a mixture of log-logistic densities,offering both symmetric and asymmetric patterns suitable for diverse real-world reliability scenarios.We establish several theoretical properties of the model,including closed-form expressions for its probability density function,cumulative distribution function,moments,hazard rate function,and quantiles.Parameter estimation is performed using seven classical estimation techniques,with extensive Monte Carlo simulations used to evaluate and compare their performance under various conditions.The practical utility and flexibility of the proposed model are illustrated using two real-world datasets from reliability and engineering applications,where the NExLL model demonstrates superior fit and predictive performance compared to existing log-logistic-basedmodels.This contribution advances the toolbox of parametric survivalmodels,offering a robust alternative formodeling complex aging and failure patterns in reliability,engineering,and other applied domains.
文摘Clustered survival data are widely observed in a variety of setting. Most survival models incorporate clustering and grouping of data accounting for between-cluster variability that creates correlation in order to prevent underestimate of the standard errors of the parameter estimators but do not include random effects. In this study, we developed a mixed-effect parametric proportional hazard (MEPPH) model with a generalized log-logistic distribution baseline. The parameters of the model were estimated by the application of the maximum likelihood estimation technique with an iterative optimization procedure (quasi-Newton Raphson). The developed MEPPH model’s performance was evaluated using Monte Carlo simulation. The Leukemia dataset with right-censored data was used to demonstrate the model’s applicability. The results revealed that all covariates, except age in PH models, were significant in all considered distributions. Age and Townsend score were significant when the GLL distribution was used in MEPPH, while sex, age and Townsend score were significant in MEPPH model when other distributions were used. Based on information criteria values, the Generalized Log-Logistic Mixed-Effects Parametric Proportional Hazard model (GLL-MEPPH) outperformed other models.
文摘We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We obtain explicit expressions for themoments,moment-generating function,asymptotic distribution,quantile function,mean deviations and distribution of order statistics.The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study.The applicability of the new model is illustrated by means of a real data set.
文摘In this paper,we studied a two-parameter transmuted model of Log-logistic distribution(LLD)using the quadratic rank transmutation map technique studied by Shaw and Buckley1 as a new survival model in medical sciences and other applied fields.Statistical properties of Transmuted LLD(TLLD)are discussed comprehensively.Robust measures of skewness and kurtosis of the proposed model have also been discussed along with graphical overview.The estimation of the model parameters is performed by Maximum Likelihood(ML)method followed by a Monte Carlo(MC)simulation procedure to investigate the performance of the ML estimators and the asymptotic confidence intervals of the parameters.Applications of the proposed model to real-life data are also presented.
文摘Home mortgage loan lending firms are exposed to many business risks.This paper focuses on the mortgage loan borrower risks and proposes a prospective loss analysis approach in regard to loan repayment defaults of borrowers.For this purpose,a predictive modeling is presented in three stages.In the first stage,occurrence of borrower defaults in a mortgage loans portfolio is modeled through the generalized linear models(GLMs)type regressions for which we specify a logistic distribution for default events.The second stage of modeling develops a survival analysis in order to estimate survival probability and hazard rate functions for individual loans.Ultimately,an expectable loss amount model is presented in the third stage as a function of conditional survival probabilities and corresponding hazard rates at loan levels.Throughout all modeling stages,a large and real data set is used as an empirical analysis case by which detailed interpretations and practical implications of the obtained results are stated.
基金supported by the Spanish Ministerio de Ciencia e Innovaciòn(PID 2020-112773 GB-I00)by Gobierno de Aragòn(ADETRE Reference GroupS39_20R).
文摘We estimate the distribution of COVID-19 mortality(measured as daily deaths)from the start of the pandemic until July 31st,2022,for six European countries and the USA.We use the Pareto,the stretched exponential,the log-normal and the log-logistic distributions as well as mixtures of the log-normal and log-logistic distributions.The main results are that the Pareto does not describe well the data and that mixture distributions tend to offer a very good fit to the data.We also compute Value-at-Risk measures as well as mortality probabilities with our estimates.We also discuss the implications of our results and findings from the point of view of public health planning and modelling.
