scholarly journals Ultimate Time Survival Probability in Three-Risk Discrete Time Risk Model

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 147 ◽  
Author(s):  
Andrius Grigutis ◽  
Jonas Šiaulys
Keyword(s):  
Discrete Time ◽  
Survival Probability ◽  
Risk Model ◽  
Time Model ◽  
Numerical Examples ◽  
Discrete Time Model ◽  
Survival Probabilities ◽  
Renewal Model ◽  
Recursive Formulas

In this paper, we prove recursive formulas for ultimate time survival probability when three random claims X , Y , Z in the discrete time risk model occur in a special way. Namely, we suppose that claim X occurs at each moment of time t ∈ { 1 , 2 , … } , claim Y additionally occurs at even moments of time t ∈ { 2 , 4 , … } and claim Z additionally occurs at every moment of time, which is a multiple of three t ∈ { 3 , 6 , … } . Under such assumptions, the model that is obtained is called the three-risk discrete time model. Such a model is a particular case of a nonhomogeneous risk renewal model. The sequence of claims has the form { X , X + Y , X + Z , X + Y , X , X + Y + Z , … } . Using the recursive formulas, algorithms were developed to calculate the exact values of survival probabilities for the three-risk discrete time model. The running of algorithms is illustrated via numerical examples.

scholarly journals The Asymptotics of Recovery Probability in the Dual Renewal Risk Model with Constant Interest and Debit Force

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Hao Wang ◽  
Lin Xu
Keyword(s):  
Asymptotic Behavior ◽  
Discrete Time ◽  
Risk Model ◽  
Continuous Time Model ◽  
Time Model ◽  
Discrete Time Model ◽  
Renewal Risk Model ◽  
Renewal Risk ◽  
Premium Income ◽  
Constant Interest

The asymptotic behavior of the recovery probability for the dual renewal risk model with constant interest and debit force is studied. By means the idea of Markov Skeleton method, we studied the times that the random premium incomes happened and transformed the continuous time model into a discrete time model. By investigating the fluctuations of this discrete time model, we obtained the asymptotic behavior when the random premium income belongs to a kind of heavy-tailed distributions.

scholarly journals SurvCNN: A Discrete Time-to-Event Cancer Survival Estimation Framework Using Image Representations of Omics Data

Cancers ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 3106
Author(s):  
Yogesh Kalakoti ◽  
Shashank Yadav ◽  
Durai Sundar
Keyword(s):  
Discrete Time ◽  
Cancer Survival ◽  
Performance Metrics ◽  
Downstream Processing ◽  
Cancer Prognosis ◽  
Precision Oncology ◽  
Omics Data ◽  
Time Model ◽  
Survival Probabilities ◽  
Image Representations

The utility of multi-omics in personalized therapy and cancer survival analysis has been debated and demonstrated extensively in the recent past. Most of the current methods still suffer from data constraints such as high-dimensionality, unexplained interdependence, and subpar integration methods. Here, we propose SurvCNN, an alternative approach to process multi-omics data with robust computer vision architectures, to predict cancer prognosis for Lung Adenocarcinoma patients. Numerical multi-omics data were transformed into their image representations and fed into a Convolutional Neural network with a discrete-time model to predict survival probabilities. The framework also dichotomized patients into risk subgroups based on their survival probabilities over time. SurvCNN was evaluated on multiple performance metrics and outperformed existing methods with a high degree of confidence. Moreover, comprehensive insights into the relative performance of various combinations of omics datasets were probed. Critical biological processes, pathways and cell types identified from downstream processing of differentially expressed genes suggested that the framework could elucidate elements detrimental to a patient’s survival. Such integrative models with high predictive power would have a significant impact and utility in precision oncology.

Non-homogeneous infinitely many sites discrete-time model with exact coalescent

2009 ◽  
Vol 33 (6) ◽  
pp. 713-732
Author(s):  
Adam Bobrowski ◽  
Marek Kimmel ◽  
Małgorzata Kubalińska
Keyword(s):  
Discrete Time ◽  
Time Model ◽  
Discrete Time Model
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