• Communications for Statistical Applications and Methods
• /
• v.14 no.3
• /
• pp.561-576
• /
• 2007

Five plotting positions are applied to the computation of probability weighted moments (PWM) on the parameters of the generalized logistic distribution. Over a range of parameter values with some finite sample sizes, the effects of five plotting positions are investigated via Monte Carlo simulation studies. Our simulation results indicate that the Landwehr plotting position frequently tends to document smaller biases than others in the location and scale parameter estimations. On the other hand, the Weibull plotting position often tends to cause larger biases than others. The plotting position (i - 0.35)/n seems to report smaller root mean square errors (RMSE) than other plotting positions in the negative shape parameter estimation under small samples. In comparison to the maximum likelihood (ML) method under the small sample, the PWM do not seem to be better than the ML estimators in the location and scale parameter estimations documenting larger RMSE. However, the PWM outperform the ML estimators in the shape parameter estimation when its magnitude is near zero. Sensitivity of right tail quantile estimation regarding five plotting positions is also examined, but superiority or inferiority of any plotting position is not observed.

• Wind and Structures
• /
• v.19 no.4
• /
• pp.371-387
• /
• 2014

Probability plotting positions are popular and used as the basis for distribution fitting and for inspecting the quality of the fit because of its simplicity. The plotting positions that lead to excellent approximation to the mean of the order statistics should be used if the objective of the fitting is to estimate quantiles. Since the mean depends on the sample size and is not amenable for simple to use closed form solution, many plotting positions have been presented in the literature, including a new plotting position that is derived based on the weighted least-squares method. In this study, the accuracy of using the new plotting position to fit the Gumbel distribution for estimating quantiles is assessed. Also, plotting positions derived by fitting the mean of the order statistics for all ranks is proposed, and an approximation to the covariance of the order statistics for the Gumbel (and Weibull) variate is given. Relative bias and root-mean-square-error of the estimated quantiles by using the proposed plotting position are shown. The use of the proposed plotting position to estimate the quantiles of annual maximum wind speed is illustrated.

• The Pure and Applied Mathematics
• /
• v.5 no.2
• /
• pp.133-142
• /
• 1998

A simple mathematical theory is developed on the periodicity of elementary polar functions. The periodicity plays an important role in efficient plotting of some closed polar curves, without the excessive use of plotting devices and materials. An efficient plotting algorithm utilizing the periodicity is proposed and its implementation by a Mathematica program is introduced for a family of closed polar functions.

• Journal of Korea Water Resources Association
• /
• v.44 no.2
• /
• pp.85-96
• /
• 2011

Probability plotting position is generally used for the graphical analysis of the annual maximum quantile and the estimation of exceedance probability to display the fitness between sample and an appropriate probability distribution. In addition, it is used to apply a specific goodness of fit test. Plotting position formula to define the probability plotting position has been studied in many researches. Especially, the GEV distribution which is an important probability distribution to analyze the frequency of hydrologic data was popular. In this study, the theoretical reduced variates are derived using the mean value of order statistics to derived an appropriate plotting position formula for the GEV distribution. In addition, various forms of plotting position formula considering various sample sizes and coefficients of skewness related with shape parameters are applied. The parameters of plotting position formulas are estimated using the genetic algorithm. The accuracy of derived plotting position formula is estimated by the errors between the theoretical reduced variates and those by various plotting position formulas including the derived ones in this study. As a result, the errors by derived plotting position formula is the smallest at the range of shape parameter with -0.25~0.10.

• Journal of Korea Water Resources Association
• /
• v.42 no.5
• /
• pp.365-374
• /
• 2009

Probability plotting positions are used for the graphical display of annual maximum rainfall or flood series and the estimation of exceedance probability of those values. In addition, plotting positions allow a visual examination of the fitness of probability distribution provided by frequency analysis for a given data. Therefore, the graphical approach using plotting position has been applied to many fields of hydrology and water resources planning. In this study, the plotting position formula for the Gumbel distribution is derived by using the order statistics and the probability weight moment of the Gumbel distribution for various sample sizes. And then, the parameters of plotting position formula for the Gumbel distribution are estimated by using genetic algorithm. The appropriate plotting position formulas for the Gumbel distribution are examined by the comparison of root mean square errors and biases between theoretical reduced Gumbel variates and those calculated from derived and existing plotting position formulas. As the results, Gringorten's plotting position formula has the smaller root mean square errors and biases than any other formulas.

• Economic and Environmental Geology
• /
• v.22 no.2
• /
• pp.167-171
• /
• 1989

Palaeomagnetic studies accompany calculation and plotting of pole position. This paper explains three graphical methods for the determination of pole position and plotting problem. It also derives the numerical formula for pole calculation and explains the method how the pole plotted on the rear hemisphere can be transformed to the frontal hemisphere, which is not clarified elsewhere.

• Proceedings of the KSRS Conference
• /
• 2002.10a
• /
• pp.786-791
• /
• 2002

Mapping systems using Satellite Imagery has not been well-established compare to conventional Arial Photograph mapping systems. In order for satellite imagery to produce a stable quality of maps, it requires to follow the standard mapping procedures. In this satellite imagery study, we proposed four methods of mapping procedures. Mapping methods were established by generating trial maps and analyzing types of input data and functions of DPW (Digital Photogrammetric Workstation). On quantitative aspect, accuracy of each steps were measured by increasing 2 GCPs each time from the minimum of 6 GCPs. In DLT, with the minimum of 10 points, RMSE is 2 pixels at most. Besides that, interpretation and stereoscopic plotting using KOMPSAT-1 imagery and other simulated imagery was performed. The tests resulted that, for KOMPSAT-1 (6.6m) stereoscopic images, the possibility of interpretation is 44.79% and possibility of stereoscopic plotting is 43.75%. In the other hand, for simulated imagery (1m), the possibility of interpretation is 60.92% and possibility of stereoscopic plotting is 55.18%.

• Korean Journal of Remote Sensing
• /
• v.18 no.1
• /
• pp.25-33
• /
• 2002

In 1799, Korea has become a country that holds Earth observation satellite in orbit as they had succeeded in the launch of KOPMSAT-1, the first Korean Earth observation satellite for the practical purpose. For the wide application of the satellite imagery, various application techniques are required, and topographic mapping is essential technique for the application in various fields. Moreover, considering that the main mission of the KOMPSAT-1 is to provide the satellite imagery for the mapping of Korean peninsula, the topographic mapping using KOMPSAT-1 EOC imagery is very significant. In this paper, we showed the possibility of digital plotting using KOMPSAT-1 EOC stereo images to produce topographic map. For the purpose, we implemented experimental stereo plotting using digital photogrammetric workstation and analyzed the procedure. As a result of this paper, we showed that some elements consist in 1:25,000 scale map can be plotted from KOMPSAT-1 Stereo images.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.29 no.5
• /
• pp.441-448
• /
• 2011

Lately, digital restitution was became common using digital aerial photos. Therefore, we can obtain three-dimensional data. As a plotting-maker is checked by naked eye, plotting original data is very useful for making reliable three-dimensional data including contour and elevation point layers. In this study, we want to make precise and accurate digital elevation model using plotting original data. Contour and elevation point layers was extracted in digital map and break line was extracted in plotting original data. And then, compared both of results. For comparison, we selected slight slope and complex topography area like a residence area, mountain and agricultural land. We extracted break line deleting layer until obtaining ideal digital elevation model. As the results, We could extract contour, elevation points, eight road and two boundary layers using break lines. And We could obtain precise elevation model. Editing break lines, the distortion of digital elevation model could be minimized in the complex and sharp slope area.

• Journal of the Korean Society for Precision Engineering
• /
• v.29 no.1
• /
• pp.33-40
• /
• 2012

The scaffold serves as 3D substrate for the cells adhesion and mechanical support for the newly grown tissue by maintaining the 3D structure for the regeneration of tissue and organ. In this paper, we proposed integrated scaffold fabrication system using multi-axis rapid prototyping (RP) technology. It can fabricate various types of scaffolds: arbitrary sculptured shape, primitive shape, and tube shape scaffolds by layered dispensing biocompatible/ biodegradable polymer strands in designated patterns. In order to fabricate the 3D scaffold, we need to generate the plotting path way for the scaffold fabrication system. We design a data processing program - scaffold plotting software, which can convert the 3D STL file, primitive and tube model images into the NC code for the system. Finally, we fabricated the customized 3D scaffolds with high accuracy using the plotting software and the fabrication system.