Regression models play a vital role in the study of data regarding survival of subjects.The Cox proportional hazards model for regression analysis has been frequently used in sur-vival modelling.In survival studies,it...Regression models play a vital role in the study of data regarding survival of subjects.The Cox proportional hazards model for regression analysis has been frequently used in sur-vival modelling.In survival studies,it is also possible that survival time may occur with multiple occurrences of event or competing risks.The situation of competing risks arises when there are more than one mutually exclusive causes of death(or failure)for the person(or subject).In this paper,we developed a parametric regression model using Gompertz distribution via the Cox proportional hazards model with competing risks.We discussed point and interval estimation of unknown parameters and cumulative cause-specific hazard function with maximum-likelihood method and Bayesian method of estimation.The Bayes estimates are obtained based on non-informative priors and symmetric as well as asym-metric loss functions.To observe the finite sample behaviour of the proposed model under both estimation procedures,we carried out a Monte Carlo simulation analysis.To demon-strate our methodology,we also included real data analysis.展开更多
Inthispaper,theoptimumtestplanandparameterestimationfor3-stepstep-stress accelerated life tests in the presence of modified progressive Type-I censoring are discussed.It is assumed that the lifetime of test units foll...Inthispaper,theoptimumtestplanandparameterestimationfor3-stepstep-stress accelerated life tests in the presence of modified progressive Type-I censoring are discussed.It is assumed that the lifetime of test units follows a Lomax distribution with log of characteristic life being quadratic function of stress level.The maximum likelihood and Bayesian method are used to obtain the point and interval estimators of the model parameters.The Bayes estimates are obtained using Markov chain Monte Carlo simulation based on Gibbs sampling.The optimum plan for 3-step step-stress test under modified progressive Type-I censoring is developed which minimizes the asymptotic variance of the maximum likelihood estimators of log of scale parameter at design stress.Finally,the numerical study with sensitivity analysis is presented to illustrate the proposed study.展开更多
This paper introduces a new family of distributions defined in terms of quantile function.The quantile function introduced here is the sum of quantile functions of life time distributions called Burr Ⅲ and Weibull.Di...This paper introduces a new family of distributions defined in terms of quantile function.The quantile function introduced here is the sum of quantile functions of life time distributions called Burr Ⅲ and Weibull.Different distributional characteristics and reliability properties are included in the study.Method of Least Square and Method of L-moments are applied to estimate the parameters of the model.Two real life data sets are used to illustrate the performance of the model.展开更多
In this paper,we propose bivariate iterated Farlie-Gumbel-Morgenstern(FGM)due to[Huang and Kotz(1984).Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions.Biometrika 71(3),633-636.https://doi.org/...In this paper,we propose bivariate iterated Farlie-Gumbel-Morgenstern(FGM)due to[Huang and Kotz(1984).Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions.Biometrika 71(3),633-636.https://doi.org/10.2307/2336577]with Rayleigh marginals.The dependence stress-strength reliability function is derived with its important reliability characteristics.Estimates of dependence reliability parameters are obtained.We analyse the effects of dependence parameters on the reliability function.We found that the upper bound of the positive correlation coefficient is attaining to 0.41 under a single iteration with Rayleigh marginals.A comprehensive comparison between classical FGM with iterated FGM copulas is graphically examined to assess the over or under estimation of reliability with respect to α and β.We propose a two-phase estimation procedure for estimating the reliability parameters.A Monte-Carlo simulation study is conducted to assess the finite sample behaviour of the proposed reliability estimators.Finally,the proposed estimators are examined and validated with real data sets.展开更多
文摘Regression models play a vital role in the study of data regarding survival of subjects.The Cox proportional hazards model for regression analysis has been frequently used in sur-vival modelling.In survival studies,it is also possible that survival time may occur with multiple occurrences of event or competing risks.The situation of competing risks arises when there are more than one mutually exclusive causes of death(or failure)for the person(or subject).In this paper,we developed a parametric regression model using Gompertz distribution via the Cox proportional hazards model with competing risks.We discussed point and interval estimation of unknown parameters and cumulative cause-specific hazard function with maximum-likelihood method and Bayesian method of estimation.The Bayes estimates are obtained based on non-informative priors and symmetric as well as asym-metric loss functions.To observe the finite sample behaviour of the proposed model under both estimation procedures,we carried out a Monte Carlo simulation analysis.To demon-strate our methodology,we also included real data analysis.
文摘Inthispaper,theoptimumtestplanandparameterestimationfor3-stepstep-stress accelerated life tests in the presence of modified progressive Type-I censoring are discussed.It is assumed that the lifetime of test units follows a Lomax distribution with log of characteristic life being quadratic function of stress level.The maximum likelihood and Bayesian method are used to obtain the point and interval estimators of the model parameters.The Bayes estimates are obtained using Markov chain Monte Carlo simulation based on Gibbs sampling.The optimum plan for 3-step step-stress test under modified progressive Type-I censoring is developed which minimizes the asymptotic variance of the maximum likelihood estimators of log of scale parameter at design stress.Finally,the numerical study with sensitivity analysis is presented to illustrate the proposed study.
文摘This paper introduces a new family of distributions defined in terms of quantile function.The quantile function introduced here is the sum of quantile functions of life time distributions called Burr Ⅲ and Weibull.Different distributional characteristics and reliability properties are included in the study.Method of Least Square and Method of L-moments are applied to estimate the parameters of the model.Two real life data sets are used to illustrate the performance of the model.
文摘In this paper,we propose bivariate iterated Farlie-Gumbel-Morgenstern(FGM)due to[Huang and Kotz(1984).Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions.Biometrika 71(3),633-636.https://doi.org/10.2307/2336577]with Rayleigh marginals.The dependence stress-strength reliability function is derived with its important reliability characteristics.Estimates of dependence reliability parameters are obtained.We analyse the effects of dependence parameters on the reliability function.We found that the upper bound of the positive correlation coefficient is attaining to 0.41 under a single iteration with Rayleigh marginals.A comprehensive comparison between classical FGM with iterated FGM copulas is graphically examined to assess the over or under estimation of reliability with respect to α and β.We propose a two-phase estimation procedure for estimating the reliability parameters.A Monte-Carlo simulation study is conducted to assess the finite sample behaviour of the proposed reliability estimators.Finally,the proposed estimators are examined and validated with real data sets.
