• Title/Summary/Keyword: two parameter exponential distribution

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Testing Exponentiality Based on EDF Statistics for Randomly Censored Data when the Scale Parameter is Unknown (척도모수가 미지인 임의중도절단자료의 EDF 통계량을 이용한 지수 검정)

  • Kim, Nam-Hyun
    • The Korean Journal of Applied Statistics
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    • v.25 no.2
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    • pp.311-319
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    • 2012
  • The simplest and the most important distribution in survival analysis is exponential distribution. Koziol and Green (1976) derived Cram$\acute{e}$r-von Mises statistic's randomly censored version based on the Kaplan-Meier product limit estimate of the distribution function; however, it could not be practical for a real data set since the statistic is for testing a simple goodness of fit hypothesis. We generalized it to the composite hypothesis for exponentiality with an unknown scale parameter. We also considered the classical Kolmogorov-Smirnov statistic and generalized it by the exact same way. The two statistics are compared through a simulation study. As a result, we can see that the generalized Koziol-Green statistic has better power in most of the alternative distributions considered.

Goodness of Fit Tests for the Exponential Distribution based on Multiply Progressive Censored Data (다중 점진적 중도절단에서 지수분포의 적합도 검정)

  • Yun, Hyejeong;Lee, Kyeongjun
    • Journal of the Korean Data Analysis Society
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    • v.20 no.6
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    • pp.2813-2827
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    • 2018
  • Progressive censoring schemes have become quite popular in reliability study. Under progressive censored data, however, some units can be failed between two points of observation with exact times of failure of these units unobserved. For example, loss may arise in life-testing experiments when the failure times of some units were not observed due to mechanical or experimental difficulties. Therefore, multiply progressive censoring scheme was introduced. So, we derives a maximum likelihood estimator of the parameter of exponential distribution. And we introduced the goodness-of-fit test statistics using order statistic and Lorenz curve. We carried out Monte Carlo simulation to compare the proposed test statistics. In addition, real data set have been analysed. In Weibull and chi-squared distributions, the test statistics using Lorenz curve are more powerful than test statistics using order statistics.

Switching and first-passage-time distributions in a two-mode ring dye laser (2모드 색소레이저 출력의 switching과 First-Passage-Time(FPT) 분포)

  • 박구동;신종태;김태수
    • Korean Journal of Optics and Photonics
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    • v.5 no.2
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    • pp.245-251
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    • 1994
  • The charateristics of switching between two modes in a ring dye laser has been analyzed by the Monte-Carlo computer simulation. The effect of including pump fluctuations in the first-passage-time (FPT) distributions was compared with the distribution with the quantum fluctuation. The results show the same tendency in both cases, such as steep increases from 0 to peak an exponential decrease in long time range. However the introduction of pumping fluctuation is turned out to shorten the mean FPT. The variation of the mean FPT is examined for the various fluctuationrelated parameters. The mean FPT is lengthened when pump parameter a is increased while it is shorted when Q. $\GAMMA$ are decreased. eased.

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Effect of Initial Crack Location on Spatial Randomness of Fatigue Crack Growth Resistance in Friction Stir Welded AA7075-T651 Plates (마찰교반용접된 AA7075-T651 판재의 피로균열전파저항의 공간적 불규칙성에 미치는 초기균열위치의 영향)

  • Kim, Seon Jin
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.38 no.9
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    • pp.999-1004
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    • 2014
  • In the present paper, the effects of initial crack location on spatial randomness of fatigue crack growth resistance (FCGR) in friction stir welded (FSWed) AA7075-T651 plates were studied. The objective of this study is to characterize the statistical properties of FCGR for three different types of initial crack location (ICL) specimens. In this work, the FCGR coefficients were treated as a spatial random process. It was found that the FCGR coefficients for all initial crack location specimens closely followed a two parameter Weibull distribution. The shape parameter of the Weibull distribution for BM-ICL specimens showed the largest value of 7.50, and that for the WM-ICL specimens showed the smallest value of 2.61. In addition, the autocorrelation functions for all the ICL specimens followed the exponential function.

Warping and porosity effects on the mechanical response of FG-Beams on non-homogeneous foundations via a Quasi-3D HSDT

  • Mokhtar Nebab;Hassen Ait Atmane;Riadh Bennai;Mouloud Dahmane
    • Structural Engineering and Mechanics
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    • v.90 no.1
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    • pp.83-96
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    • 2024
  • This paper suggests an analytical approach to investigate the free vibration and stability of functionally graded (FG) beams with both perfect and imperfect characteristics using a quasi-3D higher-order shear deformation theory (HSDT) with stretching effect. The study specifically focuses on FG beams resting on variable elastic foundations. In contrast to other shear deformation theories, this particular theory employs only four unknown functions instead of five. Moreover, this theory satisfies the boundary conditions of zero tension on the beam surfaces and facilitates hyperbolic distributions of transverse shear stresses without the necessity of shear correction factors. The elastic medium in consideration assumes the presence of two parameters, specifically Winkler-Pasternak foundations. The Winkler parameter exhibits variable variations in the longitudinal direction, including linear, parabolic, sinusoidal, cosine, exponential, and uniform, while the Pasternak parameter remains constant. The effective material characteristics of the functionally graded (FG) beam are assumed to follow a straightforward power-law distribution along the thickness direction. Additionally, the investigation of porosity includes the consideration of four different types of porosity distribution patterns, allowing for a comprehensive examination of its influence on the behavior of the beam. Using the virtual work principle, equations of motion are derived and solved analytically using Navier's method for simply supported FG beams. The accuracy is verified through comparisons with literature results. Parametric studies explore the impact of different parameters on free vibration and buckling behavior, demonstrating the theory's correctness and simplicity.

A Critical Evaluation of Dichotomous Choice Responses in Contingent Valuation Method (양분선택형 조건부가치측정법 응답자료의 실증적 쟁점분석)

  • Eom, Young Sook
    • Environmental and Resource Economics Review
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    • v.20 no.1
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    • pp.119-153
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    • 2011
  • This study reviews various aspects of model formulating processes of dichotomous choice responses of the contingent valuation method (CVM), which has been increasingly used in the preliminary feasibility test of Korea public investment projects. The theoretical review emphasizes the consistency between WTP estimation process and WTP measurement process. The empirical analysis suggests that two common parametric models for dichotmous choice responses (RUM and RWTP) and two commonly used probability distributions of random components (probit and logit) resulted in all most the same empirical WTP distributions, as long as the WTP functions are specified to be a linear function of the bid amounts. However, the efficiency gain of DB response compared to SB response were supported on the ground that the two CV responses are derived from the same WTP distribution. Moreover for the exponential WTP function which guarantees the non-negative WTP measures, sample mean WTP were quite different from median WTP if the scale parameter of WTP function turned out to be large.

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Evaluation for Rock Cleavage Using Distribution of Microcrack Spacings (II) (미세균열의 간격 분포를 이용한 결의 평가(II))

  • Park, Deok-Won
    • The Journal of the Petrological Society of Korea
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    • v.25 no.2
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    • pp.151-163
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    • 2016
  • The characteristics of the rock cleavage in Jurassic granite from Geochang were analysed. The evaluation for the three directions of rock cleavages was performed using the parameters such as (1) frequency of microcrack spacing(N), (2) total spacing(${\leq}1mm$), (3) mean spacing($S_{mean}$), (4) difference value($S_{mean}-S_{median}$) between mean spacing($S_{mean}$) and median spacing($S_{median}$), (5) density of spacing(${\rho}$), (6) difference value between two exponents for the whole range of the diagrams(${\lambda}_H-{\lambda}_L$), (7) mean value of exponent(${\lambda}_M$), (8) mean value of exponential constant($a_M$), (9) difference value between two exponents for the section under the initial points of intersection(${\lambda}t_H-{\lambda}t_L$), (10) mean value of exponent(${\lambda}t_M$) and (11) mean value of exponential constant($at_M$). The results of correlation analysis between the values of parameters for three rock cleavages and those for three planes are as follows. The values of (I) parameters(1, 2, 7 and 8) and (II) parameters(3, 4 and 5) are in orders of (I) H(hardway, (H1 + H2)/2) < G(grain, (G1 + G2)/2) < R(rift, (R1 + R2)/2) and (II) R < G < H. On the contrary, the values of the above two groups(I~II) of parameters for three planes show reverse orders. Besides, the values of parameter $6({\lambda}_H-{\lambda}_L)$, parameter $9({\lambda}t_H-{\lambda}t_L)$, parameter $10({\lambda}t_M)$ and parameter $11(at_M)$ for three planes are in orders of R(rift plane, (G1 + H2)/2) < H(hardway plane, (R2 + G2)/2) < G(grain plane, (R1 + H2)/2), H < G < R, H < R < G and R < H < G, respectively. The values of the above four parameters for three rock cleavages show the various orders of R < H < G, R < H < G, H < G < R and H < G < R, respectively. Meanwhile, the spacing values equivalent to the initial points of contact and intersection between the two directions of diagrams were derived. The above spacing values for three rock cleavages are in order of rift(R1 and R2) < grain(G1 and G2) < hardway(H1 and H2). The spacing values for three planes are in order of rift plane(G1 and H1) < hardway plane(R2 and G2) < grain plane(R1 and H2). In particular, the intersection angles for three rock cleavages and three planes are in order of rift and rift plane < hardway and hardway plane < grain and grain plane. Consequently, the two diagrams of rift(R1 and R2) and rift plane(G1 and H1) show higher frequency of the point of contact and intersection. These characteristics of change were derived through the general chart for three planes and three rock cleavages. Lastly, the correlation analysis through the values of parameters along with the distribution pattern is useful for discriminating three quarrying planes.

Evaluation for Rock Cleavage Using Distribution of Microcrack Lengths (미세균열의 길이 분포를 이용한 결의 평가)

  • Park, Deok-Won
    • The Journal of the Petrological Society of Korea
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    • v.24 no.3
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    • pp.165-180
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    • 2015
  • Jurassic granite from Geochang was analysed with respect to the characteristics of the rock cleavage. The phases of distribution of microcracks were well evidenced from the enlarged photomicrographs(${\times}6.7$) of the thin section. In this study, the length - cumulative frequency diagrams were used for expressing the distribution characteristics of microcrack. The diagrams for the six directions were arranged in the magnitude of density(${\rho}$). These diagrams show an order of H2 < H1 < G2 < G1 < R2 < R1 from the related chart. Among six diagrams, the diagram for hardway 2(H2) occupies the lowermost region on the left. On the contrary, the diagram for rift 1(R1) occupies the uppermost region on the right. Curve patterns of the two diagrams change from uniform to exponential distribution type in accordance with the increased density. The overall distribution characteristics of the diagrams were well evidenced from the magnitude of the exponent(${\lambda}$) and length of line oa related to the exponential straight line. The magnitude of exponent governing the values of slope(${\theta}$) is inversely proportional to the values of microcrack parameters such as number(N), length(L) and density. On the contrary, length of line oa is directly proportional to the values of the above three parameters. Above microcrack parameters related to the order of arrangement of diagrams show an order of hardway(H1 + H2) < grain(G1 + G2) < rift(R1 + R2). The distribution characteristics of progressive variation are found among the six diagrams. The order of arrangement of the diagrams indicates a relative magnitude of the rock cleavage. Meanwhile, the parameters such as slope, exponent, density and length of line oa were arranged in an order of H2 < H1 < G2 < G1 < R2 < R1. The variation curves of a smooth quadratic function are shown from the related chart. From the correlation chart between density and the above parameters, a common regularity following power-law correlation function was derived. Finally, the analysis for the rock cleavage was conducted through the combination between the diagram and microcrack parameter. This type of combination contribute to the progressivity in evaluation for the rock cleavage.

Comparison of Chukwooki and Modern data Using Annual Maximum Rainfall Event Series (연최대 호우사상 계열을 이용한 측우기자료 및 현대자료의 비교)

  • Park, Minkyu;Yoo, Chulsang;Kim, Hyeon Jun
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.30 no.2B
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    • pp.137-147
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    • 2010
  • In this study, Chukwooki and modern data were compared using annual maximum rainfall event series. Annual maximum series for specified rainfall duration in modern frequency analysis can not be constructed from Chukwooki data, so the concept of independent rainfall event is introduced to compare Chukwooki and modern data. Annual maximum rainfall event is determined by applying the bivariate exponential distribution and the parameters estimated annually are selected. The results using the annual parameter show that the hydrological meaning of the parameters is related to the variation of annual total rainfall amounts. For the whole independent rainfall events, the total rainfall and the rainfall intensity of Chukwooki data are greater than those of modern data, and rainfall duration of the two periods is similar. However modern annual maximum rainfall events show different characteristics that rainfall duration is much longer, rainfall intensity is similar and the total rainfall is greater than those of Chukwooki period. The increasing trend of rainfall duration and total rainfall of the modern annual rainfall events may be regarded as the one of components of the long-term cycle.

Development and Application of Diffusion Wave-based Distributed Runoff Model (확산파에 기초한 분포형 유출모형의 개발 및 적용)

  • Lee, Min-Ho;Yoo, Dong-Hoon
    • Journal of Korea Water Resources Association
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    • v.44 no.7
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    • pp.553-563
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    • 2011
  • According to the improvement of computer's performance, the development of Geographic Information System (GIS), and the activation of offering information, a distributed model for analyzing runoff has been studied a lot in recently years. The distribution model is a theoretical and physical model computing runoff as making target basin subdivided parted. In the distributed model developed by this study, the volume of runoff at the surface flow is calculated on the basis of the parameter determined by landcover data and a two-dimensional diffusion wave equation. Most of existing runoff models compute velocity and discharge of flow by applying Manning-Strickler's mean velocity equation and Manning's roughness coefficient. Manning's roughness coefficient is not matched with dimension and ambiguous at computation; Nevertheless, it is widely used in because of its convenience for use. In order to improve those problems, this study developed the runoff model by applying not only Manning-Strickler's equation but also Chezy's mean velocity equation. Furthermore, this study introduced a power law of exponential friction factor expressed by the function of roughness height. The distributed model developed in this study is applied to 6 events of fan-shape basin, oblong shape test basin and Anseongcheon basin as real field conditions. As a result the model is found to be excellent in comparison with the exiting runoff models using for practical engineering application.