• International Journal of Reliability and Applications
• /
• v.12 no.1
• /
• pp.61-77
• /
• 2011

One of the most important problems in the estimation of the parameter of the failure model, is the cost of experimental sampling units, which can be reduced by using any prior information available about ${\theta}$, and devising a two-stage pooling shrunken estimation procedure. We have proposed an estimator of the reliability function (R(t)) of the exponential model using two-stage time censored data when a prior value about the unknown parameter (${\theta}$) is available from the past. To compare the performance of the proposed estimator with the classical estimator, computer intensive calculations for bias, mean squared error, relative efficiency, expected sample size and percentage of the overall sample size saved expressions, were done for varying the constants involved in the proposed estimator (${\tilde{R}}$(t)).

• Journal of Korean Society on Water Environment
• /
• v.24 no.4
• /
• pp.430-435
• /
• 2008

In order to design Non-point source management, the aspect of statistical features of the entire precipitation data should be focused since non-point source discharge is driven by continuous rainfall runoffs. 3-parameter mixed exponential probability density function is used to establish urban stormwater capture curve instead of previous single-parameter exponential PDF. Then, recent 10-year data in Busan are applied to establish the curve. The result shows that 3-parameter mixed PDF gives better resolution.

• Journal of the Korean Statistical Society
• /
• v.20 no.1
• /
• pp.57-66
• /
• 1991

This paper deals with the problem of estimating an arbitrary piecewise continuous function of the parameter under squared error loss in the one parameter exponential family. Using Blyth's(1951) method sufficient conditions are given for the admissibility of (possibly generalized Bayes) estimators. Also, some examples are provided for normal, binomial, and gamma distributions.

• Communications for Statistical Applications and Methods
• /
• v.2 no.1
• /
• pp.176-184
• /
• 1995

In an exponential distribution, the properties of the interior and exterior trimmed means will be introduced, and reliability estimators using the two trimmed means will be compared with the UMVUE of reliability function through simulations.

• Journal of Korean Ophthalmic Optics Society
• /
• v.5 no.2
• /
• pp.145-150
• /
• 2000

The adaptation for a right source on the retina consists of the light-dark adaptation's two curves for a time by the rod-cone receptor. We obtained the adaptation for a time to measure the threshold intensities, it was two decay curves by the center of a rod-cone break. It could be represented the dark adaptation by a exponential decay function consisting of $T_{min}$, $a_r$, $a_c$, $T_{0(r)}$, $T_{0(c)}$, $t_b$, $t_c$'s parameters. The curves of a $t_b$ below and a $t_b$ above showed the adaptation sensitivity of the cone and the rod. The exponential decay function was well applied to the dark adaptation in difference retinal positions, in contrally fixated fields, in luminous, as age etc. It could be used the decay parameter as the index because of representing the properties of the dark adaptation's function.

• Proceedings of the KSME Conference
• /
• 2001.06c
• /
• pp.386-391
• /
• 2001

This paper presents a new two-point approximation method based on the exponential intervening variable. To avoid the lack of definition of the conventional exponential intervening variables due to zero- or negative-valued design variables the shifting level into each exponential intervening variable is introduced. Then a new quadratic approximation, whose Hessian matrix has only diagonal elements of different values, is proposed in terms of these intervening variables. These diagonal elements are computed in a closed form, which correct the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the original function at the previous point. Finally, the authors developed a sequential approximate optimizer, solved several typical design problems used in the literature and compared these optimization results with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

• Korean Journal of Mathematics
• /
• v.21 no.4
• /
• pp.429-437
• /
• 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.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
• /
• 2003.04a
• /
• pp.217-220
• /
• 2003

In the case of the remediation studies, push pull test is a more time and cost effective mettled than multi-well tracer test. It also gives Just as much or more information than the traditionally used methods. But the data analysis for the hydraulic parameters, there have been some defections such as underestimation of dispersivity, requirement for effective porosity, and calculation of recovery of center of mass to estimate linear velocity. In this research, Weibull distribution function is proposed to estimate the center of mass of breakthrough curve for Push pull test. The hydraulic parameter estimation using Weibull function showed more exact values of center of mass than those of exponential regression for field test data.

• Journal of the Korean Society of Environmental Restoration Technology
• /
• v.3 no.1
• /
• pp.1-9
• /
• 2000

The purpose of this study was to analyze the characteristics of soil erosion on the fill-slope of forest road by elapsed years after road construction. Thirteen plots were established on the fill-slope of the newly-constructed forest road, and surveyed for two years(1997~1998). In these plots, the data about soil erosion, surface runoff, vegetation coverage, slope structural characteristics and rainfall were collected. In 1997, the major causes for soil erosion were found by the correlation coefficients with the amount of surface runoff from the fill-slope, vegetation coverage, slope length, slope degree, total rainfall and max. 1 hour rainfall. But, in 1998, the major causes for soil erosion were vegetation coverage and slope degree. Using the stepwise multiple regression method, in 1997, the amount of soil erosion from the fill-slope was complexly expressed as a exponential function of statistically significant the amount of surface runoff from the fill-slope, total rainfall, slope degree of fill-slope and vegetation coverage, but, in 1998, simply expressed as a exponential function of vegetation coverage.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.12 no.1
• /
• pp.269-286
• /
• 2018

Signal detection in symmetric alpha-stable ($S{\alpha}S$) distributed noise is a challenging problem. This paper proposes a detector based on a decreasing exponential function (DEF). The DEF detector can effectively suppress the impulsive noise and achieve good performance in the presence of $S{\alpha}S$ noise. The analytical expressions of the detection and false alarm probabilities of the DEF detector are derived, and the parameter optimization for the detector is discussed. A performance analysis shows that the DEF detector has much lower computational complexity than the Gaussian kernelized energy detector (GKED), and it performs better than the latter in $S{\alpha}S$ noise with small characteristic exponent values. In addition, the DEF detector outperforms the fractional lower order moment (FLOM)-based detector in $S{\alpha}S$ noise for most characteristic exponent values with the same order of magnitude of computational complexity.