• Communications for Statistical Applications and Methods
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• 제25권5호
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• pp.569-575
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• 2018

Pareto distribution is important to analyze data in actuarial sciences, reliability, finance, and climatology. In general, unknown parameters of the Pareto distribution are estimated based on the maximum likelihood method that may yield inadequate inference results for small sample sizes and high percent censored data. In this paper, a new approach based on the regression framework is proposed to estimate unknown parameters of the Pareto distribution under the progressive Type-II censoring scheme. The proposed method provides a new regression type estimator that employs the spacings of exponential progressive Type-II censored samples. In addition, the provided estimator is a consistent estimator with superior performance compared to maximum likelihood estimators in terms of the mean squared error and bias. The validity of the proposed method is assessed through Monte Carlo simulations and real data analysis.

• Advances in Computational Design
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• 제7권1호
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• pp.37-56
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• 2022

Phase-type distributions are the distributions of the time to absorption in finite and absorbing Markov chains. They generalize, while at the same time, retain the tractability of the exponential distributions and their family. They are widely used as stochastic models from queuing theory, reliability, dependability, and forecasting, to computer networks, security, and computational design. The ability to fit phase-type distributions to intractable or empirical distributions is, therefore, highly desirable for many practical purposes. Many methods and tools currently exist for this fitting problem. In this paper, we present the results of our investigation on using orthogonal-distance fitting as a method for fitting phase-type distributions, together with a comparison to the currently existing fitting methods and tools.

• East Asian mathematical journal
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• 제32권5호
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• pp.659-675
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• 2016

In this paper, we study the generalized Kirchhoff type equation in the presence of past and finite history $$\large u_{tt}-M(x,t,{\tau},\;{\parallel}{\nabla}u(t){\parallel}^2){\Delta}u+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^t}\;h(t-{\tau})div[a(x){\nabla}u({\tau})]d{\tau}\\\hspace{25}-{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{-{\infty}}}^t}\;k(t-{\tau}){\Delta}u(x,t)d{\tau}+{\mid}u{\mid}^{\gamma}u+{\mu}_1u_t(x,t)+{\mu}_2u_t(x,t-s(t))=0.$$ Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the expoential decay rate of the Kirchhoff type energy.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권1호
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• pp.51-64
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• 2012

This paper provides an efficient dimension reduction algorithm of the positive realization of discrete phase type(DPH) distributions. The relationship between the representation of DPH distributions and the positive realization of the positive system is explained. The dimension of the positive realization of a discrete phase-type realization may be larger than its McMillan degree of probability generating functions. The positive realization with sufficient large dimension bound can be obtained easily but generally, the minimal positive realization problem is not solved yet. We propose an efficient dimension reduction algorithm to make the positive realization with tighter upper bound from a given probability generating functions in terms of convex cone problem and linear programming.

• 대한산업공학회지
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• 제14권2호
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• pp.81-90
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• 1988

This paper is concerned with warranty cost models for a product with two types of failure ; type 1 failures corrected by minimal repair and type 2 failures removed only by replacement. Two warranty policies involving an initial free service period followed by a pro-rata period are considered ; the difference is whether the warranty is renewed or not when type 2 failure occures during its free service period. Expected warranty costs under the two policies are obtained, and their behaviors are examined for the case where type 1 and 2 failure distributions are Weibull and exponential, respectively.

• 한국정밀공학회지
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• 제14권8호
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• pp.146-154
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• 1997

Solenoid-folw control type ABS is used with a 'dump and reapply' pressure control arrangement instead of using 2/2 (normal open/close) solenoid valves in convensional systems(sol. -sol. control type), a flow control valve is used which replaces the (no) inlet valve. The flow control valve controls fluid flow providing a nearly constant reapply rate( .theta. ) after the dump plase of ABS operation. In this study, to investigate a characteristics of brake pressure by PWM control, test rig was consisted of ABS hydraulic modulator, digital controller, pneumatic power supply and brake master cylinder. For comparison with experi- mental results, system modelling and computer simulation were performed. As a result, experiment results showed fairly agreement with the simulation. Also, it is shown that the pressure gradient (tan .theta. ) is affected by pressure, frequency, duty ratio and expressed with an exponential funtion.

• 한국지반신소재학회논문집
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• 제3권2호
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• pp.31-38
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• 2004

2종류 지오그리드의 장기안정성의 검토되었다. 멤브레인 연신형 지오그리드는 지수함수형 인장거동을, 섬유형 지오그리드는 파단점에 가까울수록 빠른 인장특성 증가를 나타내었다. 섬유형 지오그리드의 경우 가속 크리프 시험을 실시하였지만 멤브레인 연신형 지오그리드의 경우에는 열적특성 때문에 가속 크리프 시험을 실시할 수 없었다. 멤브레인 연신형 지오그리드의 크리프 변형률은 인장시험에 의한 극한변형률보다 훨씬 큰 값을 나타내었으며, 섬유형 지오그리드의 크리프 변형에 의한 감소인자는 멤브레인 연신형 지오그리드에 비해 작은 값을 나타내었다.

• 한국학교수학회논문집
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• 제19권2호
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• pp.177-196
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• 2016

본 연구에서는 수능의 수학영역의 출제 유형이나 난이도 등이 고등학교 문과계열 수학 교수 학습과정에 어떠한 영향을 미치는지 알아보기 위하여 최근 5년간(2012~2016학년도) 수능 수학 A형(나형)의 출제유형과 난이도를 살펴보고, 출제유형과 난이도가 고등학교 문과계열 수학 내신 상위권 학생들의 수학 학습 내용에 어떠한 영향을 미치는지에 대해 연구하였다. 그 결과 다음과 같은 결론을 얻었다. 첫째, 고등학교 수학 내신이 상위권인 학생들의 수능등급을 결정하는 오답률 90% 이상인 문항은 지수함수와 로그함수 단원에 편중되어 출제되었다. 둘째, 수능 상위권 학생들은 수능 등급 향상을 위하여 지수함수와 로그함수 단원을 중점적으로 학습해야 할 단원으로 인식하고 있었다.

• Journal of the Korean Data and Information Science Society
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• 제26권1호
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• pp.271-280
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• 2015

In this paper, the maximum likelihood estimators for parameters are derived under three step-stress accelerated life tests for Type-I hybrid censored data. The exponential distribution and the cumulative exposure model are considered based on the assumption that a log quadratic relationship exits between stress and the mean lifetime ${\theta}$. The test plan to search optimal stress change times minimizing the asymptotic variance of maximum likelihood estimators are presented. A numerical example to illustrate the proposed inferential procedures and some simulation results to investigate the sensitivity of the optimal stress change times by the guessed parameters are given.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1033-1047
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• 2009

In this paper, we consider a m-type risk model with Markov-modulated premium rate. A integral equation for the conditional ruin probability is obtained. A recursive inequality for the ruin probability with the stationary initial distribution and the upper bound for the ruin probability with no initial reserve are given. A system of Laplace transforms of non-ruin probabilities, given the initial environment state, is established from a system of integro-differential equations. In the two-state model, explicit formulas for non-ruin probabilities are obtained when the initial reserve is zero or when both claim size distributions belong to the $K_n$-family, n $\in$ $N^+$ One example is given with claim sizes that have exponential distributions.