• Title/Summary/Keyword: Asymptotic normal

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ANALYSIS OF A STAGE-STRUCTURED PREDATOR-PREY SYSTEM WITH IMPULSIVE PERTURBATIONS AND TIME DELAYS

  • Song, Xinyu;Li, Senlin;Li, An
    • Journal of the Korean Mathematical Society
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    • v.46 no.1
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    • pp.71-82
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    • 2009
  • In this paper, a stage-structured predator-prey system with impulsive perturbations and time delays is presented to investigate the ecological problem of how a pest population and natural enemy population can coexist. Sufficient conditions are obtained using a discrete dynamical system determined by a stroboscopic map, which guarantee that a 'predator-extinction' periodic solution is globally attractive. When the impulsive period is longer than some time threshold or the impulsive harvesting rate is below a control threshold, the system is permanent. Our results provide some reasonable suggestions for pest management.

On Quantifies Estimation Using Ranked Samples with Some Applications

  • Samawi, Hani-M.
    • Journal of the Korean Statistical Society
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    • v.30 no.4
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    • pp.667-678
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    • 2001
  • The asymptotic behavior and distribution for quantiles estimators using ranked samples are introduced. Applications of quantiles estimation on finding the normal ranges (2.5% and 97.5% percentiles) and the median of some medical characteristics and on finding the Hodges-Lehmann estimate are discussed. The conclusion of this study is, whenever perfect ranking is possible, the relative efficiency of quantiles estimation using ranked samples relative to SRS is high. This may translates to large savings in cost and time. Also, this conclusion holds even if the ranking is not perfect. Computer simulation results are given and real data from lows 65+ study is used to illustrate the method.

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A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model

  • Asghari, P.;Fakoor, V.;Sarmad, M.
    • Communications for Statistical Applications and Methods
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    • v.21 no.2
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    • pp.115-124
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    • 2014
  • In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if $Y{\geq}T$, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to $n^{-1/6}$ modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.

On testing NBUL aging class of life distribution

  • Hassan, M.Kh.;El-Din, M.M. Mohie;Abu-Youssef, S.E.
    • International Journal of Reliability and Applications
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    • v.15 no.1
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    • pp.1-9
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    • 2014
  • Let X and $X_t$ denote the lifetime and the residual life at age t, respectively. X is said to be a NBUL (new better than used in Laplace transform order) random variable if $X_t$ is smaller than X in Laplace order, i.e., $X_t{\leq}_{LT}X$. We propose a new test statistics for testing exponentiality versus NBUL class of life distribution. The tests by Hollender and Proschan (1975) and the generalized Hollender and Proschan test by Ains and Mitra (2011) are considered as special cases of the our of test statistics. Our proposed test statistics is simple, consistent and asymptotically normal. Efficiency and powers of the test statistics for some commonly used distributions in reliability are discussed. Finally, real examples are presented to illustrate the theoretical results.

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Statistical Estimation for Hazard Function and Process Capability Index under Bivariate Exponential Process (이변량 지수 공정 하에서 위험함수와 공정능력지수에 대한 통계적 추정)

  • Cho, Joong-Jae;Kang, Su-Mook;Park, Byoung-Sun
    • Communications for Statistical Applications and Methods
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    • v.16 no.3
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    • pp.449-461
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    • 2009
  • Higher sigma quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. The process capability indices and the sigma level $Z_{st}$ ave been widely used in six sigma industries to assess process performance. Most evaluations on process capability indices focus on statistical estimation under normal process which may result in unreliable assessments of process performance. In this paper, we consider statistical estimation for bivariate VPCI(Vector-valued Process Capability Index) $C_{pkl}=(C_{pklx},\;C_{pklx})$ under Marshall and Olkin (1967)'s bivariate exponential process. First, we derive some limiting distribution for statistical inference of bivariate VPCI $C_{pkl}$. And we propose two asymptotic normal confidence regions for bivariate VPCI $C_{pkl}$. The proposed method may be very useful under bivariate exponential process. A numerical result based on our proposed method shows to be more reliable.

On the Plug-in Estimator and its Asymptotic Distribution Results for Vector-Valued Process Capability Index Cpmk (2차원 벡터 공정능력지수 Cpmk의 추정량과 극한분포 이론에 관한 연구)

  • Cho, Joong-Jae;Park, Byoung-Sun
    • Communications for Statistical Applications and Methods
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    • v.18 no.3
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    • pp.377-389
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    • 2011
  • A higher quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. The third generation index $C_{pmk}$ is more powerful than two useful indices $C_p$ and $C_{pk}$ that have been widely used in six sigma industries to assess process performance. In actual manufacturing industries, process capability analysis often entails characterizing or assessing processes or products based on more than one engineering specification or quality characteristic. Since these characteristics are related, it is a risky undertaking to represent the variation of even a univariate characteristic by a single index. Therefore, the desirability of using vector-valued process capability index(PCI) arises quite naturally. In this paper, we consider more powerful vector-valued process capability index $C_{pmk}$ = ($C_{pmkx}$, $C_{pmky}$)$^t$ that consider the univariate process capability index $C_{pmk}$. First, we examine the process capability index $C_{pmk}$ and plug-in estimator $\hat{C}_{pmk}$. In addition, we derive its asymptotic distribution and variance-covariance matrix $V_{pmk}$ for the vector valued process capability index $C_{pmk}$. Under the assumption of bivariate normal distribution, we study asymptotic confidence regions of our vector-valued process capability index $C_{pmk}$ = ($C_{pmkx}$, $C_{pmky}$)$^t$.

Analysis of Inclined Crack Extension in Orthotropic Solids Under Biaxial Loading (2축하중을 받는 직교이방성체내 경사균열진전의 해석)

  • Lim, Won-Kyun;Choi, Seung-Yong
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.26 no.6
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    • pp.993-1000
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    • 2002
  • The objective of this work is to develop the capability to analyze accurately the mixed-mode propagation of a crack in composite structures with elastic orthotropic material stiffness properties and anisotropic material strength characteristics. In order to develop the capability to fully analyze fracture growth and failure in anisotropic structures, we examined the fundamental problem of mixed mode fracture by carrying out the analysis on orthotropic materials with an inclined crack subject to biaxial loading. Our goal here is to include an additional term in the asymptotic expansion of the crack tip stress field and to show that the direction of crack initiation can be significantly affected by that term. We employ the normal stress ratio theory to predict the direction of crack extension. It is shown that the angle of crack extension can be altered by horizontal loads and the use of second order term in the series expansion is important f3r the accurate determination of crack growth direction.

Experimental studies on the axisymmetric sphere-wall interaction in Newtonian and non-Newtonian fluids

  • Lee, Sang-Wang;Sohn, Sun-Mo;Ryu, Seung-Hee;Kim, Chongyoup;Song, Ki-Won
    • Korea-Australia Rheology Journal
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    • v.13 no.3
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    • pp.141-148
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    • 2001
  • In this research, experimental studies leave been performed on the hydrodynamic interaction between a spherical particle and a plane wall by measuring the force between the particle and wall. To approach the system as a resistance problem, a servo-driving system was set-up by assembling a microstepping motor, a ball screw and a linear motion guide for the particle motion. Glycerin and dilute solution of polyacrylamide in glycerin were used as Newtonian and non-Newtonian fluids, respectively. The polymer solution behaves like a Boger fluid when the concentration is 1,000 ppm or less. The experimental results were compared with the asymptotic solution of Stokes equation. The result shows that fluid inertia plays all important role in the particle-wall interaction in Newtonian fluid. This implies that the motion of two particles in suspension is not reversible even in Newtonian fluid. In non-Newtonian fluid, normal stress difference and viscoelasticity play important roles as expected. In the dilute solution weak shear thinning and the migration of polymer molecules in the inhomogeneous flow field also affect the physic of the problem.

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Estimating Confidence Interval of Value of Travel Time(II) (통행시간가치의 신뢰구간 추정(II))

  • 조종래;박철규
    • Journal of Korean Society of Transportation
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    • v.17 no.2
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    • pp.193-198
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    • 1999
  • An asymptotic distribution of the ratio of two normal vectors is estimated. Using the estimated asymptotic distribution, an approximation method to estimate confidence interval of passenger's value of travel time is proposed. As a result of empirical study the 95% confidence interval of value of travel time of home-to-work trips in city of Seoul is estimated at ₩7341.25$\pm$1945.05/hr.

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A Novel Carrier-to-noise Power Ratio Estimation Scheme with Low Complexity for GNSS Receivers (GNSS 수신기를 위한 낮은 복잡도를 갖는 새로운 반송파 대 잡음 전력비 추정기법)

  • Yoo, Seungsoo;Baek, Jeehyeon;Yeom, Dong-Jin;Jee, Gyu-In;Kim, Sun Yong
    • Journal of Institute of Control, Robotics and Systems
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    • v.20 no.7
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    • pp.767-773
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    • 2014
  • The carrier-to-noise power ratio is a key parameter for determining the reliability of PVT (Position, Velocity, and Time) solutions which are obtained by a GNSS (Global Navigation Satellite System) receiver. It is also used for locking a tracking loop, deciding the re-acquisition process, and processing advanced navigation in the receiver subsystem. The representative carrier-to-noise power ratio estimation schemes are the narrowband-wideband power ratio method (NW), the MM (Moment Method), and Beaulieu's method (BL). The NW scheme is the most classical one for commercial GNSS receivers. It is often used as an authoritative benchmark for assessing carrier-to-noise power estimation schemes. The MM scheme is the least biased solution among them, and the BL scheme is a simpler scheme than the MM scheme. This paper focuses on the less biased estimation with low complexity when the residual phase noise remains, then proposes a novel carrier-to-noise power ratio estimation scheme with low complexity for GNSS receivers. The asymptotic bias of the proposed scheme is derived and compared with others, and the simulation results demonstrate that the complexity of the proposed scheme is lowest among them, while the estimation performance of the proposed scheme is similar to those of the BL and MM schemes in normal and high gained reception environments.