The aim of this paper is to present generalized log-Lindely (GLL) distribution, as a new model, and find doubly truncated generalized log-Lindely (DTGLL) distribution, truncation in probability distributions may occur...The aim of this paper is to present generalized log-Lindely (GLL) distribution, as a new model, and find doubly truncated generalized log-Lindely (DTGLL) distribution, truncation in probability distributions may occur in many studies such as life testing, and reliability. We illustrate the applicability of GLL and DTGLL distributions by Real data application. The GLL distribution can handle the risk rate functions in the form of panich and increase. This property makes GLL useful in survival analysis. Various statistical and reliability measures are obtained for the model, including hazard rate function, moments, moment generating function, mean and variance, quantiles function, Skewness and kurtosis, mean deviations, mean inactivity time and strong mean inactivity time. The estimation of model parameters is justified by the maximum Likelihood method. An application to real data shows that DTGLL distribution can provide better suitability than GLL and some other known distributions.展开更多
An AR(1) model with ARCH(1) error structure is known as the first-order double autoregressive (DAR(1)) model. In this paper, a conditional likelihood based method is proposed to obtain inference for the two scalar par...An AR(1) model with ARCH(1) error structure is known as the first-order double autoregressive (DAR(1)) model. In this paper, a conditional likelihood based method is proposed to obtain inference for the two scalar parameters of interest of the DAR(1) model. Theoretically, the proposed method has rate of convergence O(n-3/2). Applying the proposed method to a real-life data set shows that the results obtained by the proposed method can be quite different from the results obtained by the existing methods. Results from Monte Carlo simulation studies illustrate the supreme accuracy of the proposed method even when the sample size is small.展开更多
A survival analysis on a data set of 295 early breast cancer patients is performed in this study. A new proportional hazards model, hypertabastic model was applied in the survival analysis. We assume a proportional ha...A survival analysis on a data set of 295 early breast cancer patients is performed in this study. A new proportional hazards model, hypertabastic model was applied in the survival analysis. We assume a proportional hazards model, and select two sets of risk factors for death and metastasis for breast cancer patients respectively by using standard variable selection methods. To evaluate the performance of the new model and compare it with other popular distributions, Cox, Weibull and log-logistic models were fitted to the data besides the hypertabastic model. Result shows that the hypertabastic proportional hazards model outperformed all the comparison models and provided the best fit for the breast cancer data. In addition, we observed that the gene expression variable, wound response signature, combined with other clinical variables, can provide an effective model to predict the overall survival and hazard rate for breast cancer patients.展开更多
文摘The aim of this paper is to present generalized log-Lindely (GLL) distribution, as a new model, and find doubly truncated generalized log-Lindely (DTGLL) distribution, truncation in probability distributions may occur in many studies such as life testing, and reliability. We illustrate the applicability of GLL and DTGLL distributions by Real data application. The GLL distribution can handle the risk rate functions in the form of panich and increase. This property makes GLL useful in survival analysis. Various statistical and reliability measures are obtained for the model, including hazard rate function, moments, moment generating function, mean and variance, quantiles function, Skewness and kurtosis, mean deviations, mean inactivity time and strong mean inactivity time. The estimation of model parameters is justified by the maximum Likelihood method. An application to real data shows that DTGLL distribution can provide better suitability than GLL and some other known distributions.
文摘An AR(1) model with ARCH(1) error structure is known as the first-order double autoregressive (DAR(1)) model. In this paper, a conditional likelihood based method is proposed to obtain inference for the two scalar parameters of interest of the DAR(1) model. Theoretically, the proposed method has rate of convergence O(n-3/2). Applying the proposed method to a real-life data set shows that the results obtained by the proposed method can be quite different from the results obtained by the existing methods. Results from Monte Carlo simulation studies illustrate the supreme accuracy of the proposed method even when the sample size is small.
文摘A survival analysis on a data set of 295 early breast cancer patients is performed in this study. A new proportional hazards model, hypertabastic model was applied in the survival analysis. We assume a proportional hazards model, and select two sets of risk factors for death and metastasis for breast cancer patients respectively by using standard variable selection methods. To evaluate the performance of the new model and compare it with other popular distributions, Cox, Weibull and log-logistic models were fitted to the data besides the hypertabastic model. Result shows that the hypertabastic proportional hazards model outperformed all the comparison models and provided the best fit for the breast cancer data. In addition, we observed that the gene expression variable, wound response signature, combined with other clinical variables, can provide an effective model to predict the overall survival and hazard rate for breast cancer patients.
