• Title/Summary/Keyword: exponential hazard rate

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Moments of Order Statistics from Doubly Truncated Linear-Exponential Distribution

  • Saran, Jagdish;Pushkarna, Narinder
    • Journal of the Korean Statistical Society
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    • v.28 no.3
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    • pp.279-296
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    • 1999
  • In this paper we establish some recurrence relations for both single and product moments of order statistics from a doubly truncated linear- exponential distribution with increasing hazard rate. These recurrence relations would enable one to compute all the higher order moments of order statistics for all sample sizes from those of the lower order in a simple recursive way. In addition, percentage points of order statistics are also discussed. These generalize the corresponding results for the linear- exponential distribution with increasing hazard rate derived by Balakrishnan and Malik(1986)

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Reliability estimation and ratio distribution in a general exponential distribution

  • Lee, Chang-Soo;Moon, Yeung-Gil
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.3
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    • pp.623-632
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    • 2014
  • We shall consider the estimation for the parameter and the right tail probability in a general exponential distribution. We also shall consider the estimation of the reliability P(X < Y ) and the skewness trends of the density function of the ratio X=(X+Y) for two independent general exponential variables each having different shape parameters and known scale parameter. We then shall consider the estimation of the failure rate average and the hazard function for a general exponential variable having the density function with the unknown shape and known scale parameters, and for a bivariate density induced by the general exponential density.

SEQUENTIAL INTERVAL ESTIMATION FOR THE EXPONENTIAL HAZARD RATE WHEN THE LOSS FUNCTION IS STRICTLY CONVEX

  • Jang, Yu Seon
    • Korean Journal of Mathematics
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    • v.21 no.4
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    • pp.429-437
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    • 2013
  • Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be independent and identically distributed random variables having common exponential density with unknown mean ${\mu}$. In the sequential confidence interval estimation for the exponential hazard rate ${\theta}=1/{\mu}$, when the loss function is strictly convex, the following stopping rule is proposed with the half length d of prescribed confidence interval $I_n$ for the parameter ${\theta}$; ${\tau}$ = smallest integer n such that $n{\geq}z^2_{{\alpha}/2}\hat{\theta}^2/d^2+2$, where $\hat{\theta}=(n-1)\bar{X}{_n}^{-1}/n$ is the minimum risk estimator for ${\theta}$ and $z_{{\alpha}/2}$ is defined by $P({\mid}Z{\mid}{\leq}{\alpha}/2)=1-{\alpha}({\alpha}{\in}(0,1))$ Z ~ N(0, 1). For the confidence intervals $I_n$ which is required to satisfy $P({\theta}{\in}I_n){\geq}1-{\alpha}$. These estimated intervals $I_{\tau}$ have the asymptotic consistency of the sequential procedure; $$\lim_{d{\rightarrow}0}P({\theta}{\in}I_{\tau})=1-{\alpha}$$, where ${\alpha}{\in}(0,1)$ is given.

Change-Point Estimation and Bootstrap Confidence Regions in Weibull Distribution

  • Jeong, Kwang-Mo
    • Journal of the Korean Statistical Society
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    • v.28 no.3
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    • pp.359-370
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    • 1999
  • We considered a change-point hazard rate model generalizing constant hazard rate model. This type of model is very popular in the sense that the Weibull and exponential distributions formulating survival time data are the special cases of it. Maximum likelihood estimation and the asymptotic properties such as the consistency and its limiting distribution of the change-point estimator were discussed. A parametric bootstrap method for finding confidence intervals of the unknown change-point was also suggested and the proposed method is explained through a practical example.

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Abundance Estimation of the Finless Porpoise, Neophocaena phocaenoides, Using Models of the Detection Function in a Line Transect (Line Transect에서 발견율함수 추정에 사용되는 모델에 따른 상괭이, Neophocaena phocaenoides의 자원개체수 추정)

  • Park, Kyum-Joon;Kim, Zang-Geun;Zhang, Chang-Ik
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.40 no.4
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    • pp.201-209
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    • 2007
  • Line transect sampling in a sighting survey is one of most widely used methods for assessing animal abundance. This study applied distance data, collected from three sighting surveys using line transects for finless porpoise that were conducted in 2004 and 2005 off the west coast of Korea, to four models (hazard-rate, uniform, half-normal and exponential) that can use a variety of detection functions, g (x). The hazard-rate model, a derived model for the detection function, should have a shoulder condition chosen using the AIC (Akaike Information Criterion), as the most suitable model. However, it did not describe a shoulder shape for the value of g(x) near the track tine and underestimated g (x), just as the exponential model did. The hazard-rate model showed a bias toward overestimating the densities of finless porpoises with a higher coefficient of variation (CV) than the other models did. The uniform model underestimated the densities of finless porpoise but had the lowest CV. The half-normal model described a detection function with a shape similar to that of the uniform model. The half-normal model was robust for finless porpoise data and should be able to avoid density underestimation. The estimated abundance of finless porpoise was 3,602 individuals (95% CI=1,251-10,371) inshore in 2005 and 33,045 individuals (95% CI=24,274-44,985) offshore in 2004.

Comparing the Bayesian Estimates of Hazard Rate of Mixed Distribution and Hazard Rates by the MLE Method

  • Suneung Ahn;Kim, Hyunmook
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2003.11a
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    • pp.263-266
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    • 2003
  • This paper is intended to compare between the Bayesian estimates of hazard rate and the hazard rates of mixed distributions. In estimating hazard rates, especially when the MLE method is used, such difficulties as a lack of data and the existence of censored data make it difficult to estimate the rates. For this reason, the estimates of hazard rate based on the Bayesian approach are introduced. For the simplicity, the exponential and gamma distributions are adopted as a sampling distribution and its natural conjugate prior distribution, respectively.

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Estimation of hazard function and hazard change-point for the rectal cancer data (직장암 데이터에 대한 위험률 함수 추정 및 위험률 변화점 추정)

  • Lee, Sieun;Shim, Byoung Yong;Kim, Jaehee
    • Journal of the Korean Data and Information Science Society
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    • v.26 no.6
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    • pp.1225-1238
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    • 2015
  • In this research, we fit various survival models and conduct tests and estimation for the hazard change-point with the rectal cancer data. By the log-rank tests, at significance level ${\alpha}=0.10$, survival functions are significantly different according to the uniporter of glucose (GLUT1), clinical stage (cstage) and pathologic stage (ypstage). From the Cox proportional hazard model, the most significant covariates are GLUT1 and ypstage. Assuming that the rectal cancer data follows the exponential distribution, we estimate one hazard change-point using Matthews and Farewell (1982), Henderson (1990) and Loader (1991) methods.

Accelerated Life Tests under Uniform Stress Distribution (스트레스함수가 균등분포인 가속수명시험)

  • 원영철
    • Journal of the Korea Safety Management & Science
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    • v.2 no.2
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    • pp.71-83
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    • 2000
  • This paper presents accelerated life tests for Type I censoring data under probabilistic stresses. Probabilistic stress, $S_j$, is the random variable for stress influenced by test environments, test equipments, sampling devices and use conditions. The hazard rate, ,$theta_j$, is the random variable of environments and the function of probabilistic stress. Also it is assumed that the general stress distribution is uniform, the life distribution for the given hazard rate, $\theta$, is exponential and inverse power law model holds. In this paper, we obtained maximum likelihood estimators of model parameters and the mean life in use stress condition.

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Accelerated Life Tests under Gamma Stress Distribution (스트레스함수가 감마분포인 가속수명시험)

  • 원영철
    • Journal of the Korea Safety Management & Science
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    • v.4 no.3
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    • pp.59-66
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    • 2002
  • This paper presents accelerated life tests for Type I censoring data under probabilistic stresses. Probabilistic stress, S, is the random variable for stress influenced by test environments, test equipments, sampling devices and use conditions. The hazard rate, $\theta$ is a random variable of environments and a function of probabilistic stress. In detail, it is assumed that the hazard rate is linear function of the stress, the general stress distribution is a gamma distribution and the life distribution for the given hazard rate, $\theta$is an exponential distribution. Maximum likelihood estimators of model parameters are obtained, and the mean life in use stress condition is estimated. A hypothetical example is given to show its applicability.

Hazard Rate Estimation from Bayesian Approach (베이지안 확률 모형을 이용한 위험률 함수의 추론)

  • Kim, Hyun-Mook;Ahn, Seon-Eung
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.28 no.3
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    • pp.26-35
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    • 2005
  • This paper is intended to compare the hazard rate estimations from Bayesian approach and maximum likelihood estimate(MLE) method. Hazard rate frequently involves unknown parameters and it is common that those parameters are estimated from observed data by using MLE method. Such estimated parameters are appropriate as long as there are sufficient data. Due to various reasons, however, we frequently cannot obtain sufficient data so that the result of MLE method may be unreliable. In order to resolve such a problem we need to rely on the judgement about the unknown parameters. We do this by adopting the Bayesian approach. The first one is to use a predictive distribution and the second one is a method called Bayesian estimate. In addition, in the Bayesian approach, the prior distribution has a critical effect on the result of analysis, so we introduce the method using computerized-simulation to elicit an effective prior distribution. For the simplicity, we use exponential and gamma distributions as a likelihood distribution and its natural conjugate prior distribution, respectively. Finally, numerical examples are given to illustrate the potential benefits of the Bayesian approach.