Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data
Obalowu Job,
Adeyinka Solomon Ogunsanya
Issue:
Volume 8, Issue 1, March 2022
Pages:
1-13
Received:
13 February 2022
Accepted:
8 March 2022
Published:
15 March 2022
Abstract: A four-parameter continuous probability model called the Weibull log-logistic {Exponential} distribution (WLLED) was introduced and studied in this research using T-log-logistic {Exponential} distribution via T-R{Y} framework to extend the two-parameter log-logistic distribution. The objective of this research is to explore the versatility and flexibility of the log-logistic and Weibull distributions in modeling lifetime data. Some basic structural properties which include the reliability measures and hazard function, cumulative hazard function, Moment, Quantile, skewness, kurtosis, mixture representation, order statistics and asymptotic behavior of the WLLED were obtained and established. The shape of the new four parameter distribution is also investigated. A simulation study was conducted to evaluate the MLE estimates, bias, and standard error for various parameter combinations and different sample sizes. The efficiency of the WLLE distribution was compared with other related distribution from the literature using five goodness-of-fit statistics: AIC, CAIC and BIC, Anderson-Darling A* and Cramér-Von Mises W*, methods of comparison. The method of maximum likelihood estimation was proposed in estimating its parameters. An application to the survival times of 121 patients with breast cancer dataset was provided and the WLLED displays a good fit. Finally, it is recommended that the WLLED can be used for modeling positively skewed real-life data.
Abstract: A four-parameter continuous probability model called the Weibull log-logistic {Exponential} distribution (WLLED) was introduced and studied in this research using T-log-logistic {Exponential} distribution via T-R{Y} framework to extend the two-parameter log-logistic distribution. The objective of this research is to explore the versatility and flex...
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Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms
Issue:
Volume 8, Issue 1, March 2022
Pages:
14-23
Received:
17 March 2022
Accepted:
6 April 2022
Published:
23 April 2022
Abstract: Due to the rapid development of information technology and data acquisition technology, the model which only considers the linear main effect can not provide accurate prediction results, and the interaction between the predictor and response variables can not be ignored, so the variable selection problem of the model with interaction terms has become an important research topic in the statistical analysis today. In this paper, we discuss the problem of variable selection for a partially linear model with interaction terms using the profile forward selection method under high dimensional data. We propose the two-stage interactive selection algorithm (iPFST) under strong genetic condition and the profile forward selection algorithm (iPFSM) under marginality principle respectively. Theoretically, we use the consistency of profile estimators to prove that profile estimators have uniform convergence rate, and use the screening consistency to prove that iPFST algorithm and iPFSM algorithm can uniformly identify all important linear main effect terms and important interaction effect terms with probability 1. Seven regularization conditions for the theorem are given. Numerical simulation shows the superiority of iPFST and iPFSM in variable selection, and the two algorithms are compared, then iPFST algorithm is better than iPFSM algorithm. Finally, we give detailed technical proof.
Abstract: Due to the rapid development of information technology and data acquisition technology, the model which only considers the linear main effect can not provide accurate prediction results, and the interaction between the predictor and response variables can not be ignored, so the variable selection problem of the model with interaction terms has beco...
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