• 대한수학회지
• /
• 제60권3호
• /
• pp.537-564
• /
• 2023

In this paper, we are mainly concerned with two-sided estimates for transition probabilities of symmetric Markov chains on ℤ^d, whose one-step transition probability is comparable to |x - y|^-dϕ_j (|x - y|)^-1 with ϕ_j being a positive regularly varying function on [1, ∞) with index α ∈ [2, ∞). For upper bounds, we directly apply the comparison idea and the Davies method, which considerably improves the existing arguments in the literature; while for lower bounds the relation with the corresponding continuous time symmetric Markov chains are fully used. In particular, our results answer one open question mentioned in the paper by Murugan and Saloff-Coste (2015).

• 한국정보통신학회논문지
• /
• 제26권2호
• /
• pp.317-320
• /
• 2022

This paper studies real-time error in the context of monitoring a symmetric binary information source over a delay system. To obtain the average real-time error, the delay system is modeled and analyzed as a discrete time Markov chain with a finite state space. Numerical analysis is performed on various system parameters such as state transition probabilities of information source, transmission times, and transmission frequencies. Given state transition probabilities and transmission times, we investigate the relationship between the transmission frequency and the average real-time error. The results can be used to investigate the relationship between real-time errors and age of information.

• Nuclear Engineering and Technology
• /
• 제53권2호
• /
• pp.357-367
• /
• 2021

In general, common cause failures (CCFs) have been modeled with the assumption that components within the same group are symmetric. This assumption reduces the number of parameters required for the CCF probability estimation and allows us to use a parametric model, such as the alpha factor model. Although there are various asymmetric conditions in nuclear power plants (NPPs) to be addressed, the traditional CCF models are limited to symmetric conditions. Therefore, this paper proposes the copulabased CCF model to deal with asymmetric as well as symmetric CCFs. Once a joint distribution between the components is constructed using copulas, the proposed model is able to provide the probability of common cause basic events (CCBEs) by formulating a system of equations without symmetry assumptions. In addition, Bayesian inferences for the parameters of the marginal and copula distributions are introduced and Markov Chain Monte Carlo (MCMC) algorithms are employed to sample from the posterior distribution. Three example cases using simulated data, including asymmetry conditions in total failure probabilities and/or dependencies, are illustrated. Consequently, the copula-based CCF model provides appropriate estimates of CCFs for asymmetric conditions. This paper also discusses the limitations and notes on the proposed method.

• Journal of applied mathematics & informatics
• /
• 제42권4호
• /
• pp.819-829
• /
• 2024

This paper delves into an examination of both non-Bayesian and Bayesian estimation techniques for determining the Topp-leone inverse Weibull distribution parameters based on progressive Type-II censoring. The first approach employs expectation maximization (EM) algorithms to derive maximum likelihood estimates for these variables. Subsequently, Bayesian estimators are obtained by utilizing symmetric and asymmetric loss functions such as Squared error and Linex loss functions. The Markov chain Monte Carlo method is invoked to obtain these Bayesian estimates, solidifying their reliability in this framework.

• Communications for Statistical Applications and Methods
• /
• 제28권2호
• /
• pp.99-118
• /
• 2021

In this paper, we introduce an extended form of the inverse power Lomax model via Marshall-Olkin approach. We call it the Marshall-Olkin inverse power Lomax (MOIPL) distribution. The four- parameter MOIPL distribution is very flexible which contains some former and new models. Vital properties of the MOIPL distribution are affirmed. Maximum likelihood estimators and approximate confidence intervals are considered under Type I censored samples. Maximum likelihood estimates are evaluated according to simulation study. Bayesian estimators as well as Bayesian credible intervals under symmetric loss function are obtained via Markov chain Monte Carlo (MCMC) approach. Finally, the flexibility of the new model is analyzed by means of two real data sets. It is found that the MOIPL model provides closer fits than some other models based on the selected criteria.

• 응용통계연구
• /
• 제33권2호
• /
• pp.123-136
• /
• 2020

하나의 개체에서 여러가지 측정치가 동시에 관찰되는 경우는 다양한 연구 분야에서 흔히 나타난다. 발달 독성학 연구에서는 특정 독성 물질의 각기 다른 수준에 노출된 임신한 어미 쥐에 대해 기형인 태아의 존재와 태아의 무게가 동시에 측정된다. 이런 두 변수를 결합하여 모형화하는 것은 각기 독립적인 두 모형으로 분석하는 것보다 더 효율적인 결과를 낸다고 알려져 있다. 대부분의 결합 모형은 정규분포를 랜덤효과로 가정하여 분석한다. 그러나 발달 독성학 연구에서처럼 반응변수들의 분포가 독성 물질이 변함에 따라 불규칙하게 변하는 경우 정규분포의 가정으로는 그 특징을 잡아낼 수 없게 된다. 본 논문에서는 이진수 자료와 연속형 자료에 대해 비대칭 로짓 모형을 사용한 베이지안 결합모형을 제시한다. 본 모형은 비대칭 로짓 모형을 사용함으로써 반응변수의 분포의 형태가 독성 물질의 수준에 따라 대칭/비대칭의 형태를 자유롭게 띨 수 있는 장점을 가지고 있다. 모형의 적합성을 살펴보기 위해 발달 독성학 연구에서 독성 물질 DEHP에 적용하여 그 결과를 확인해본다.