• Communications for Statistical Applications and Methods
• /
• v.19 no.2
• /
• pp.277-286
• /
• 2012

For credit assessment models, the ROC curves evaluate the classification performance using two univariate cumulative distribution functions of the false positive rate and true positive rate. In this paper, it is extended to two bivariate normal distribution functions of default and non-default borrowers; in addition, the bivariate ROC curves are proposed to represent the joint cumulative distribution functions by making use of the linear function that passes though the mean vectors of two score random variables. We explore the classification performance based on these ROC curves obtained from various bivariate normal distributions, and analyze with the corresponding AUROC. The optimal threshold could be derived from the bivariate ROC curve using many well known classification criteria and it is possible to establish an optimal cut-off criteria of bivariate mixture distribution functions.

• Journal of Korean Society of Transportation
• /
• v.27 no.2
• /
• pp.23-34
• /
• 2009

This paper is described as an experimental analysis for the probabilistic directional design hour volume estimation. The main objective of this paper is to derive acceptable design rankings, PK factors, and PD factors. In order to determine an appropriate distribution for acceptable design rankings, 12 probability distribution functions were employed. The parameters were estimated based on the method of maximum likelihood. The goodness of fit test was performed with a Kolmogorov-Smirnov test. The Beta General distribution among the probability distributions was selected as an appropriate model for 2 lane roadways. On the other hand, the Weibull distribution is superior for 4 lanes. The method of the inverse cumulative distribution function came up with an acceptable design ranking of design for LOS D. An acceptable design ranking of 2 lanes is 190, while an acceptable design ranking for 4 lanes is 164. The PK factor and PD factor of 2 lanes was elicited for 0.119 (0.100-0.139) and 0.568 (0.545-0.590), respectively. On the other hand, the PK factor and PD factor for 4 lanes was elicited as 0.106 (0.097-0.114) and 0.571 (0.544-0.598), respectively.

• Journal of Wetlands Research
• /
• v.17 no.3
• /
• pp.251-263
• /
• 2015

This study suggested a novel approach of estimating the optimal probability density function (OPDF) of the annual maximum rainfall time series (AMRT) combining the L-moment ratio diagram and the geographical information system. This study also reported several interesting geographical characteristics of the AMRT in Korea. To achieve this purpose, this study determined the OPDF of the AMRT with the duration of 1-, 3-, 6-, 12-, and 24-hours using the method of L-moment ratio diagram for each of the 67 rain gages in Korea. Then, a map with the Thiessen polygons of the 67 rain gages colored differently according the different type of the OPDF, was produced to analyze the spatial trend of the OPDF. In addition, this study produced the color maps which show the fitness of a given probability density function to represent the AMRT. The study found that (1) both L-skewness and L-kurtosis of the AMRT have clear geographical trends, which means that the extreme rainfall events are highly influenced by geography; (2) the impact of the altitude on these two rainfall statistics is greater for the mountaneous region than for the non-mountaneous region. In the mountaneous region, the areas with higher altitude are more likely to experience the less-frequent and strong rainfall events than the areas with lower altitude; (3) The most representative OPDFs of Korea except for the Southern edge are Generalized Extreme Value distribution and the Generalized Logistic distribution. The AMRT of southern edge of Korea was best represented by the Generalized Pareto distribution.

• Economic and Environmental Geology
• /
• v.46 no.4
• /
• pp.313-327
• /
• 2013

In the study, three-dimensional geostatistical simulations on McMurray Formation which is the largest oil sand reservoir in Athabasca area, Canada were performed, and the optimal site for steam assisted gravity drainage (SAGD) was selected based on the predictions. In the selection, the factors related to the vertical extendibility of steam chamber were considered as the criteria for an optimal site. For the predictions, 110 borehole data acquired from the study area were analyzed in the Markovian transition probability (TP) framework and three-dimensional distributions of the composing media were predicted stochastically through an existing TP based geostatistical model. The potential of a specific medium at a position within the prediction domain was estimated from the ensemble probability based on the multiple realizations. From the ensemble map, the cumulative thickness of the permeable media (i.e. Breccia and Sand) was analyzed and the locations with the highest potential for SAGD applications were delineated. As a supportive criterion for an optimal SAGD site, mean vertical extension of a unit permeable media was also delineated through transition rate based computations. The mean vertical extension of a permeable media show rough agreement with the cumulative thickness in their general distribution. However, the distributions show distinctive disagreement at a few locations where the cumulative thickness was higher due to highly alternating juxtaposition of the permeable and the less permeable media. This observation implies that the cumulative thickness alone may not be a sufficient criterion for an optimal SAGD site and the mean vertical extension of the permeable media needs to be jointly considered for the sound selections.

• Journal of Korean Tunnelling and Underground Space Association
• /
• v.24 no.1
• /
• pp.1-13
• /
• 2022

A weighted linear combination of seismic fragility models previously developed for cut-and-cover railway tunnels was presented and the appropriateness of the combined model was evaluated. The seismic fragility function is expressed in the form of a cumulative probability function of the lognormal distribution based on the peak ground acceleration. The model uncertainty can be reduced by combining models independently developed. Equal weight is applied to four models. The new seismic fragility function was developed for each damage level by determining the median and standard deviation, which are model metrics. Comparing fragility curves developed for other bored tunnels, cut-and-cover tunnels for high-speed railway system have a similar level of fragility. We postulated that this is due to the high seismic design standard for high-speed railway tunnel.

• The KIPS Transactions:PartA
• /
• v.9A no.2
• /
• pp.267-270
• /
• 2002

The evaluation of the cumulative distribution function of the noncentral $\chi^2$ distribution is required in approximate determination of the power of the $\chi^2$ test. This article provides an algorithm for evaluating the noncentral $\chi^2$ distribution function in terms of a single "central" $\chi^2$ distribution function and compared various approximations.ximations.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.30 no.5D
• /
• pp.497-504
• /
• 2010

In this paper, the author presents a reliability estimation technique to analyze the effects of traffic loads on pavement mean life based on the national highway database of Suwon and Uijeongbu region from 1999 to 2008. The estimation of the mean life, its standard deviation and reliability for pavement sections are calculated by using an appropriate distribution, Lognormal distribution, based on reliability theory. Furthermore, the probability paper method and Maximum likelihood estimation are both used to estimate parameters. The author found that mean life of newly constructed sections and over-layed sections is about 6.5 to 7.9 years and 7.3 to 9.1 years, respectively. The author also ascertained that the results of cumulative failure probability for pavement life between the proposed methods and observed data are similar. Such an assessment methodology and measures based on reliability theory can provide useful information for maintenance plans in pavement management systems as long as additional life data on pavement sections are accumulated.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.23 no.9A
• /
• pp.2305-2312
• /
• 1998

This paper analyzed the delay characteristics of speech packets in virtual cellular network(VCN). The probability distribution of packet delay is obtained using the markov chain model when periodic speech packets are transmitted by slotted-ALOHA protocol. The effects of probility of capture and retransmission policy on the performance were also analyzed. At first, the probability cumulative function of packet delay is calculated from the probability of capture as a function of location of mobile terminal. In order to investigate the effects of backoff delay, we defined a parameter NPr, where N is the period (frame size) of the speech packets and Pr is the retransmission probability for each speech packet. We also obtained the 1% outage delay for various frame size N.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.27 no.4B
• /
• pp.345-352
• /
• 2002

In this paper, in order to evaluate the performance of IS-95 system reverse link in white gaussian noise and rayleigh fading environment, we suggest epochal proposal to improve computer run-time and its efficiency is verified in terms of the number of samples. MC(Monte Carlo) simulation is the most popular simulation technique lately, but MC simulation requires a number of samples at low bit error rate. Therefore, MC cannot avoid the limit of computer run-time. To alleviate these problems, we apply the suggested method called central moment technique to the reverse link of the IS-95 system and can obtain discrete probability mass functions from Nth order central moments of the less number of received signal samples than those required in MC. Continuous cumulative probability distribution function can be accurately estimated by using interpolation and the improvement effect for the number of samples is proven.

• Journal of Advanced Marine Engineering and Technology
• /
• v.28 no.6
• /
• pp.993-999
• /
• 2004

The estimation of fatigue life at the design stage of membrane type LNG tank is very important in order to arrive at feasible and cost effective solutions considering the total lifetime of the tank. In this study, the practical procedure of fatigue life prediction by use of cumulative damage factors based on Miner-Palmgren hypothesis and probability density function has been shown with the corner region of Gaz Transport Membrane type LNG tank being used as an example. In particular the parameters of Weibull distribution that determine the stress spectrum are discussed. The main results obtained from this study are as follows: 1. The recommended value for the shape parameter of Weibull distribution for the LNG tank is 1.1 in case of using the direct calculation method proposed in this study. 2. The calculated fatigue life is influenced by the shape parameter of Weibull distribution and stress block. The safe fatigue design can be achieved by using higher value of shape parameter and the stress blocks divided into more stress blocks.