scholarly journals Exact Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censored Competing Risks Data

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2005
Author(s):  
Youngseuk Cho ◽  
Kyeongjun Lee
Keyword(s):  
Risk Model ◽  
Moment Generating Function ◽  
Conditional Moment ◽  
Exponential Parameter ◽  
Exact Inference ◽  
Scale Parameters ◽  
Lower Confidence Bound ◽  
Competing Risks Data ◽  
Conditional Moment Generating Function ◽  
Censoring Scheme

It is known that the lifetimes of items may not be recorded exactly. In addition, it is known that more than one risk factor (RisF) may be present at the same time. In this paper, we discuss exact likelihood inference for competing risk model (CoRiM) with generalized adaptive progressive hybrid censored exponential data. We derive the conditional moment generating function (ConMGF) of the maximum likelihood estimators of scale parameters of exponential distribution (ExpD) and the resulting lower confidence bound under generalized adaptive progressive hybrid censoring scheme (GeAdPHCS). From the example data, it can be seen that the PDF of MLE is almost symmetrical.

scholarly journals Exact Likelihood Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censoring

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1149 ◽  
Author(s):  
Hyojin Lee ◽  
Kyeongjun Lee
Keyword(s):  
Scale Parameter ◽  
Moment Generating Function ◽  
Likelihood Inference ◽  
Exponential Parameter ◽  
Hybrid Censoring ◽  
Lower Confidence ◽  
Lower Confidence Bound ◽  
New Type ◽  
The Moment ◽  
Censoring Scheme

In this paper, we propose a new type censoring scheme named a generalized adaptive progressive hybrid censoring scheme (GenAdPrHyCS). In this new type censoring scheme, the experiment is assured to stop at a pre-assigned time. This censoring scheme is designed to correct the drawbacks in the AdPrHyCS. Furthermore, we discuss inference for one parameter exponential distribution (ExD) under GenAdPrHyCS. We derive the moment generating function of the maximum likelihood estimator (MLE) of scale parameter of ExD and the resulting lower confidence bound under GenAdPrHyCS.

Fuzzy GERT model based on z-tag and its application in weapon equipment management

2021 ◽  
pp. 1-17
Author(s):  
Na Zhang ◽  
Shuli Yan ◽  
Zhigeng Fang ◽  
Baohua Yang
Keyword(s):  
Time Dependence ◽  
Network Model ◽  
Execution Time ◽  
Arrival Time ◽  
Moment Generating Function ◽  
Equipment Management ◽  
Practical Application ◽  
Fuzzy Information ◽  
Conditional Moment ◽  
Conditional Moment Generating Function

In view of the situation that tasks or activities in the GERT model may have multiple realizations, this paper explores the time dependence of each repeated execution node under the condition of fuzzy information, and studies the characteristics of the z-tag fuzzy GERT model and its analytic algorithm. Firstly, the F-GERT model related to the number of executions of activities is defined, and the simplified rules, related properties and theorems of the network model are examined. Secondly, solving algorithm, conditional moment generating function and process arrival time of the F-GERT model for repeated execution time are studied. Finally, the application of F-GERT queuing system based on element execution time in weapon equipment management is discussed. The feasibility and effectiveness of the model and algorithm are verified by the practical application of the project.

scholarly journals EXPLICIT COMPUTATIONS FOR A FILTERING PROBLEM WITH POINT PROCESS OBSERVATIONS WITH APPLICATIONS TO CREDIT RISK

2011 ◽  
Vol 25 (3) ◽  
pp. 393-418 ◽  
Author(s):  
Vincent Leijdekker ◽  
Peter Spreij
Keyword(s):  
Credit Risk ◽  
Point Process ◽  
Generating Function ◽  
Moment Generating Function ◽  
Cox Process ◽  
Risk Modeling ◽  
Conditional Moment ◽  
Credit Risk Modeling ◽  
Conditional Moment Generating Function ◽  
Filtering Problem

We consider the filtering problem for a doubly stochastic Poisson or Cox process, where the intensity follows the Cox–Ingersoll–Ross model. In this article we assume that the Brownian motion, which drives the intensity, is not observed. Using filtering theory for point process observations, we first derive the dynamics for the intensity and its moment-generating function, given the observations of the Cox process. A transformation of the dynamics of the conditional moment-generating function allows us to solve in closed form the filtering problem, between the jumps of the Cox process as well as at the jumps, which constitutes the main contribution of the article. Assuming that the initial distribution of the intensity is of the Gamma type, we obtain an explicit solution to the filtering problem for all t>0. We conclude the article with the observation that the resulting conditional moment-generating function at time t, after Nt jumps, corresponds to a mixture of Nt+1 Gamma distributions. Currently, the model that we analyze has become popular in credit risk modeling, where one uses the intensity-based approach for the modeling of default times of one or more companies. In this approach, the default times are defined as the jump times of a Cox process. In such a model, one only has access to observations of the Cox process, and thus filtering comes in as a natural technique in credit risk modeling.

scholarly journals Exact Likelihood Inference for a Competing Risks Model with Generalized Type II Progressive Hybrid Censored Exponential Data

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 887
Author(s):  
Subin Cho ◽  
Kyeongjun Lee
Keyword(s):  
Competing Risks ◽  
Real Data ◽  
Likelihood Inference ◽  
Type Ii ◽  
Conditional Moment ◽  
Data Set ◽  
Scale Parameters ◽  
Competing Risks Model ◽  
Censoring Scheme ◽  
Generalized Type

In many situations of survival and reliability test, the withdrawal of units from the test is pre-planned in order to to free up testing facilities for other tests, or to save cost and time. It is known that several risk factors (RiFs) compete for the immediate failure cause of items. In this paper, we derive an inference for a competing risks model (CompRiM) with a generalized type II progressive hybrid censoring scheme (GeTy2PrHCS). We derive the conditional moment generating functions (CondMgfs), distributions and confidence interval (ConfI) of the scale parameters of exponential distribution (ExDist) under GeTy2PrHCS with CompRiM. A real data set is analysed to illustrate the validity of the method developed here. From the data, it can be seen that the conditional PDFs of MLEs is almost symmetrical.

SOME REMARKS ON BLACKWELL–ROSS MARTINGALE INEQUALITIES

2006 ◽  
Vol 21 (1) ◽  
pp. 109-115 ◽  
Author(s):  
Rasul A. Khan
Keyword(s):  
Generating Function ◽  
Suitable Condition ◽  
Moment Generating Function ◽  
Conditional Moment ◽  
Martingale Differences ◽  
Martingale Inequalities ◽  
Conditional Moment Generating Function

Under a suitable condition on the conditional moment generating function of the martingale differences, an exponential supermartingale is used to generalize certain martingale inequalities due to Blackwell and Ross.

scholarly journals Different Approaches to Estimation of the Gompertz Distribution under the Progressive Type-II Censoring Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kyeongjun Lee ◽  
Jung-In Seo
Keyword(s):  
Nuisance Parameter ◽  
Estimation Method ◽  
Real Data ◽  
Type Ii ◽  
Gompertz Distribution ◽  
Type Ii Censoring ◽  
Scale Parameters ◽  
Progressive Type ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

This paper provides an estimation method for an unknown parameter by extending weighted least-squared and pivot-based methods to the Gompertz distribution with the shape and scale parameters under the progressive Type-II censoring scheme, which induces a consistent estimator and an unbiased estimator of the scale parameter. In addition, a way to deal with a nuisance parameter is provided in the pivot-based approach. For evaluation and comparison, the Monte Carlo simulations are conducted, and real data are analyzed.

scholarly journals Competing Risks Model with Partially Step-Stress Accelerate Life Tests in Analyses Lifetime Chen Data under Type-II Censoring Scheme

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 192-199 ◽  
Author(s):  
Hanaa H. Abu-Zinadah ◽  
Neveen Sayed-Ahmed
Keyword(s):  
Risk Factors ◽  
Risk Model ◽  
Asymptotic Distributions ◽  
Likelihood Method ◽  
Model Parameters ◽  
Type Ii ◽  
Monte Carlo Simulation Study ◽  
Type Ii Censoring ◽  
Life Tests ◽  
Censoring Scheme

Abstract The experiment design may need a stress level higher than use condition which is called accelerate life tests (ALTs). One of the most ALTs appears in different applications in the life testes experiment is partially step stress ALTs. Also, the experiment items is failure with several fatal risk factors, the only one is caused to failure which called competing risk model. In this paper, the partially step-stress ALTs based on Type-II censoring scheme is adopted under the different risk factors belong to Chen lifetime distributions. Under this assumption, we will estimate the model parameters of the different causes with the maximum likelihood method. The two, asymptotic distributions and the parametric bootstrap will be used to build each confidence interval of the model parameters. The precision results will be assessed through Monte Carlo simulation study.

scholarly journals On a Dual Model with Barrier Strategy

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yuzhen Wen ◽  
Chuancun Yin
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Generating Function ◽  
Risk Model ◽  
Moment Generating Function ◽  
Dual Model ◽  
Barrier Strategy ◽  
Dividend Payments ◽  
The Moment

We consider the dual of the generalized Erlang(n)risk model with a barrier dividend strategy. We derive integro-differential equations with boundary conditions satisfied by the expectation of the sum of discounted dividends until ruin and the moment-generating function of the discounted dividend payments until ruin, respectively. The results are illustrated by several examples.

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