• Title/Summary/Keyword: moment generating function

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Study on a Simulator for Generating Side Walking Path of the Biped Walking Robot (이족보행로봇의 횡보행 경로생성을 위한 시뮬레이터 연구)

  • Choi, Hyeung-Sik;Jeon, Chang-Hoon;Kang, Jin-Il
    • Journal of Advanced Marine Engineering and Technology
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    • v.32 no.8
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    • pp.1285-1295
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    • 2008
  • A research on a simulator for a side walking path of a 16 degree-of-freedom (d.o.f) biped walking robot(BWR) which is composed of 4 d.o.f upper-part body and 12 d.o.f lower-part of the body is presented. For generation of stable side walking motion, the kinematics, dynamics and the zero moment of point(ZMP) of the BWR were analyzed analytically and included in the simulator. To operate the motion simulator for stable side walking of the BWR, a graphic user interface program was developed which needs inputs for the side distance between legs, base joint angle, walking type, and walking velocity. The simulator was developed to generate joint angle data of legs for side walking, and the data are transmitted to the BWR for stable side walking. In the simulator, a new path function for smooth walking motion was proposed and applied to the simulator and actual motion of a BWR. Also for actual side walking, an algorithm for estimating backlashes of the actuating joint motors was proposed and included in the simulator. To validate the performance of the proposed motion simulator, the simulator was operated and its side walking data of the simulator were generated for a period of side walking.

CONSTRAINTS ON PRE-INFLATION COSMOLOGY AND DARK FLOW

  • MATHEWS, GRANT J.;LAN, N.Q.;KAJINO, T.
    • Publications of The Korean Astronomical Society
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    • v.30 no.2
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    • pp.309-313
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    • 2015
  • If the present universe is slightly open then pre-inflation curvature would appear as a cosmic dark-flow component of the CMB dipole moment. We summarize current cosmological constraints on this cosmic dark flow and analyze the possible constraints on parameters characterizing the pre-inflating universe in an inflation model with a present-day very slightly open ${\Lambda}CDM$ cosmology. We employ an analytic model to show that for a broad class of inflation-generating effective potentials, the simple requirement that the observed dipole moment represents the pre-inflation curvature as it enters the horizon allows one to set upper and lower limits on the magnitude and wavelength scale of pre-inflation fluctuations in the inflaton field and the curvature parameter of the pre-inflation universe, as a function of the fraction of the total initial energy density in the inflaton field. We estimate that if the current CMB dipole is a universal dark flow (or if it is near the upper limit set by the Planck Collaboration) then the present constraints on ${\Lambda}CDM$ cosmological parameters imply rather small curvature ${\Omega}_k{\sim}0.1$ for the pre-inflating universe for a broad range of the fraction of the total energy in the inflaton field at the onset of inflation. Such small pre-inflation curvature might be indicative of open-inflation models in which there are two epochs of inflation.

모멘트 생성 함수 기법을 이용한 유연 제조 셀의 해석적 성능 평가

  • 박용수;김종원
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1996.04a
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    • pp.506-511
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    • 1996
  • The performance evaluation of flexible manufacturing systems or cells at the stages of design and planning is one of important issues in manufacturing. For that reason, Guo has presented an approachbased on moment generating function and generalized stochastic PetriNets for performance analysis. In this paper, Buo's approach is extended tothe cases of flexible manufacturing cell including one machining center with a local buffer, AS/RS(Automatic Storage and Retrieval System), set-up station and AGV(Automated Guided Vehicle). Then the performance measures from this approach is compared with simulation. The major advantage ofthis method over existing performance evaluation methods is the ability to compute analytic solutions for performance measures.

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Performance Evaluation of FMS Using Generalized Stochastic Petri Nets (Generalized Stochastic 페트리네트를 이용한 유연생산시스템의 성능평가)

  • 서경원;박용수;박홍성;김종원
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1994.10a
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    • pp.653-657
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    • 1994
  • A symbolic performance analysis approach for flexible for manufactring systems (FMS) can be formulated based on the integration of Petri Nets (PN) and moment generating function (MGF) concept. In this method, generalized stochastic Petri Nets are used to define performance models for FMS, then MGF nased approach for evaluating stochastic PN is used to derive performance parameters of PN, and finally system performance is calculated. A GSPN model of machine cell is shown to illustrate the proposed method for evaluating such performance indices as production rate, utilization, work-in-process and lead time. The major advantage of this method over existing performance evaluation of FMS is the ability to compute symbolic solutions for performance. Finally future research toward automating performance measure for GSPN models of FMS is discussed.

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A Study on the manufacturing process using the sensitivity analysis of stochastic network (감도분석에 의한 제조공정연구)

  • 박기주
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.24 no.63
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    • pp.65-77
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    • 2001
  • A more technical perspective is needed in estimating the effect of the Manufacturing Process for improving the Productivity, there are many statistical evaluation methods, convenience sampling, frequencies, histogram, QC seven tools, control chart etc. It is more important for the companies to use six sigma to reduce defective and improve the process control than the technical definition as a disciplined quantitative approach for improvement of process control and a new way of quality innovation. Process network analysis is a technique which has the potentiality for a wide use to improve the manufacturing process which other techniques can't be used to analyze effectively. It has some problems to analyze the process with feedback loops. The branch probabilities during quality inspections depend upon the number of times the product has been rejected. This paper presents how to improve the manufacturing process by statistical process control using branch probabilities, Moment Generating Function(MGF) and Sensitivity Equation.

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On NBUmgf class at specific age

  • Gadallah, A.M.
    • International Journal of Reliability and Applications
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    • v.17 no.2
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    • pp.107-119
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    • 2016
  • A new concept of aging classes namely new better (worse) than used at age $t_0$ in moment generating function order, $NBU_{mgf}-t_0$ ($NWU_{mgf}-t_0$) is introduced. For the classes $NBU_{mgf}-t_0$ ($NWU_{mgf}-t_0$), preservation under convolution, mixture, mixing and the homogeneous Poisson shock model are studied. In the sequel, nonparametric test is proposed, the asymptotic normality of the class is established and the asymptotic null variance is estimated. The percentiles and powers of this test are tabulated. The asymptotic efficiencies for some alternatives distributions are derived. Finally sets of real data are used as examples to elucidate the use of the proposed test in practical application.

The transmuted GEV distribution: properties and application

  • Otiniano, Cira E.G.;de Paiva, Bianca S.;Neto, Daniele S.B. Martins
    • Communications for Statistical Applications and Methods
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    • v.26 no.3
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    • pp.239-259
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    • 2019
  • The transmuted generalized extreme value (TGEV) distribution was first introduced by Aryal and Tsokos (Nonlinear Analysis: Theory, Methods & Applications, 71, 401-407, 2009) and applied by Nascimento et al. (Hacettepe Journal of Mathematics and Statistics, 45, 1847-1864, 2016). However, they did not give explicit expressions for all the moments, tail behaviour, quantiles, survival and risk functions and order statistics. The TGEV distribution is a more flexible model than the simple GEV distribution to model extreme or rare events because the right tail of the TGEV is heavier than the GEV. In addition the TGEV distribution can adjusted various forms of asymmetry. In this article, explicit expressions for these measures of the TGEV are obtained. The tail behavior and the survival and risk functions were determined for positive gamma, the moments for nonzero gamma and the moment generating function for zero gamma. The performance of the maximum likelihood estimators (MLEs) of the TGEV parameters were tested through a series of Monte Carlo simulation experiments. In addition, the model was used to fit three real data sets related to financial returns.

Simulation of the Phase-Type Distribution Based on the Minimal Laplace Transform (최소 표현 라플라스 변환에 기초한 단계형 확률변수의 시뮬레이션에 관한 연구)

  • Sunkyo Kim
    • Journal of the Korea Society for Simulation
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    • v.33 no.1
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    • pp.19-26
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    • 2024
  • The phase-type, PH, distribution is defined as the time to absorption into a terminal state in a continuous-time Markov chain. As the PH distribution includes family of exponential distributions, it has been widely used in stochastic models. Since the PH distribution is represented and generated by an initial probability vector and a generator matrix which is called the Markovian representation, we need to find a vector and a matrix that are consistent with given set of moments if we want simulate a PH distribution. In this paper, we propose an approach to simulate a PH distribution based on distribution function which can be obtained directly from moments. For the simulation of PH distribution of order 2, closed-form formula and streamlined procedures are given based on the Jordan decomposition and the minimal Laplace transform which is computationally more efficient than the moment matching methods for the Markovian representation. Our approach can be used more effectively than the Markovian representation in generating higher order PH distribution in queueing network simulation.

Performance Analysis of Distributed Antenna Systems with Antenna Selection over MIMO Rayleigh Fading Channel

  • Yu, Xiangbin;Tan, Wenting;Wang, Ying;Liu, Xiaoshuai;Rui, Yun;Chen, Ming
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.8 no.9
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    • pp.3016-3033
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    • 2014
  • The downlink performance of distributed antenna systems (DAS) with antennas selection is investigated in Rayleigh fading multicell environment, and the corresponding system capacity and bit error rate (BER) analysis are presented. Based on the moment generating function, the probability density function (PDF) and cumulative distribution function (CDF) of the effective signal to interference plus noise ratio (SINR) of the system are first derived, respectively. Then, with the available CDF and PDF, the accurate closed-form expressions of average channel capacity and average BER are further derived for exact performance evaluation. To simplify the expression, a simple closed-form approximate expression of average channel capacity is obtained by means of Taylor series expansion, with the performance results close to the accurate expression. Besides, the system outage capacity is analyzed, and an accurate closed-form expression of outage capacity probability is derived. These theoretical expressions can provide good performance evaluation for DAS downlink. It can be shown by simulation that the theoretical analysis and simulation are consistent, and DAS with antenna selection outperforms that with conventional blanket transmission. Moreover, the system performance can be effectively improved as the number of receive antennas increases.

Bit Error Probability of Noncoherent M-ary Orthogonal Modulation over Generalized Fading Channels

  • Simon, Marvin K.;Alouini, Mohamed-Slim
    • Journal of Communications and Networks
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    • v.1 no.2
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    • pp.111-117
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    • 1999
  • Using a method recently reported in the literature for analyzing the bit error probability (BEP) performance of noncoherent Mary orthogonal signals with square-law combining in the presence of independent and identically distributed Nakagami-m faded paths, we are able to reformulate this method so as to apply to a generalized fading channel in which the fading in each path need not be identically distributed nor even distributed ac-cording to the same family of distribution. The method leads to exact expressions for the BEP in the form of a finite-range integral whose integrand involves the moment generating function of the combined signal-to-noise ratio and which can therefore be readily evaluated numerically. The mathematical formalism is illustrated by applying the method to some selected numerical examples of interest showing the impact of the multipath intensity profile (MIP) as well as the fading correlation profile (FCP) on the BEP performance of M-ary orthogonal signal over Nakagami-m fading channels. Thses numerical results show that both MIP and FCP induce a non-negligible degradition in the BEP and have therefore to be taken into account for the accurate prediction of the performance of such systems.

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