• Communications for Statistical Applications and Methods
• /
• 제18권4호
• /
• pp.485-493
• /
• 2011

The proportional likelihood ratio order is an extension of the likelihood ratio order for the non-negative absolutely continuous random variables. In addition, the Lindley distribution has been over looked as a mixture of two exponential distributions due to the popularity of the exponential distribution. In this paper, we first recalled the above concepts and then obtained various properties of the Lindley distribution due to the proportional likelihood ratio order. These results are more general than the likelihood ratio ordering aspects related to this distribution. Finally, we discussed the proportional likelihood ratio ordering in view of the weighted version of the Lindley distribution.

• Journal of the Korean Data and Information Science Society
• /
• 제10권1호
• /
• pp.243-250
• /
• 1999

We consider $Y=X{\lambda}Z,\;{\lambda}>0$, where X and Z are independent random variables, and Y is the length biased distribution or the equilibrium distribution of X. The purpose of this paper is to consider the distribution of X or Y when the distribution of Z is given and the distribution of Z when the distribution of X or Y is given, In particular, we obtain that the necessary and sufficient conditions for X to be $X^{2}({\upsilon})\;is\;Z{\sim}X^{2}(2)\;and\;for\;Z\;to\;be\;X^{2}(1)\;is\;X{\sim}IG({\mu},\;{\mu}^{2}/{\lambda})$, where $IG({\mu},\;{\mu}^{2}/{\lambda})$ is two-parameter inverse Gaussian distribution. Also we show that X is smaller than Y in the reverse Laplace transform ratio order if and only if $X_{e}$ is smaller than $Y_{e}$ in the Laplace transform ratio order. Finally, we can get the results that if X is smaller than Y in the Laplace transform ratio order, then $Y_{L}$ is smaller than $X_{L}$ in the Laplace transform order, and that if X is smaller than Y in the reverse Laplace transform ratio order, then $_{\mu}X_{L}$ is smaller than $_{\nu}Y_{L}$ in the Laplace transform order.

• Journal of Power System Engineering
• /
• 제10권4호
• /
• pp.99-104
• /
• 2006

Young's modulus of composite has been predicted by Eshelby's equivalent inclusion method modified with Mori-Tanaka's mean field theory, where short fibers of aspect ratio distribution are assumed to be aligned. Young's modulus of the composite is predicted with the smallest class interval for simulating the actual distribution of fiber aspect ratio, which is compared with that computed using different class intervals. Young's modulus of the composite predicted with mean aspect ratio or the largest class interval is overestimated by the maximum 10%. As the class interval of short fibers for predicting Young's modulus decreases, the predicted results show good agreements with those obtained using the actual distribution of fiber aspect ratio. It can be finally concluded from the study that if and only if the class interval of short fiber normalized by the maximum aspect ratio is smaller than 0.1, the predicted results are consistent with those obtained using the actual distribution of aspect ratio.

• Journal of the Korean Data and Information Science Society
• /
• 제21권5호
• /
• pp.967-972
• /
• 2010

We shall consider estimations of an exponetiated parameter of the exponentiated Pareto distribution with known scale and threshold parameters. A quotient distribution of two independent exponentiated Pareto random variables is obtained. We also derive the distribution of the ratio of two independent exponentiated Pareto random variables.

• The Korean Journal of Applied Statistics
• /
• 제25권1호
• /
• pp.101-114
• /
• 2012

In car insurance, the loss ratio is the ratio of total losses paid out in claims divided by the total earned premiums. In order to minimize the loss to the insurance company, estimating extreme quantiles of loss ratio distribution is necessary because the loss ratio has essential prot and loss information. Like other types of insurance related datasets, the distribution of the loss ratio has heavy-tailed distribution. The Peaks over Threshold(POT) and the Hill estimator are commonly used to estimate extreme quantiles for heavy-tailed distribution. This article compares and analyzes the performances of various kinds of parameter estimating methods by using a simulation and the real loss ratio of car insurance data. In addition, we estimate extreme quantiles using the Hill estimator. As a result, the simulation and the loss ratio data applications demonstrate that the POT method estimates quantiles more accurately than the Hill estimation method in most cases. Moreover, MLE, Zhang, NLS-2 methods show the best performances among the methods of the GPD parameters estimation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 한국소음진동공학회 2006년도 추계학술대회논문집
• /
• pp.562-566
• /
• 2006

Lightweight body can cause a low stiffness due to the decrease of panel thickness and reinforcing member. The other way, high stiffness body demands an increase of mass. Front pillar section area is decreased due to driver's visual field. Global vehicle stiffness is affected by stiffness distribution ratio between upper part and lower part at side body structure. This paper will describe a process used to evaluate the stiffness distribution ratio based on research of strain energy analysis of the tip rotation method. In addition, optimum design schemes are presented for high stiffness and lightweight body structure considering the investigated stiffness distribution ratio. In this way the designer will be aided by a defined design guide and a set of supporting tool to help him work towards a good design

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• 제17권10호
• /
• pp.901-906
• /
• 2007

Lightweight body due to the decrease of panel thickness and reinforcing member might cause low stiffness. On the other hand, high stiffness body requires an increase of mass. Front pillar section area has been decreased for increasing the driver's visual field. Global vehicle stiffness is affected by stiffness distribution ratio between upper part and lower part at a side body structure. This paper describes a process used to evaluate the stiffness distribution ratio based on strain energy. In addition, optimum design schemes are presented for high stiffness and lightweight body structure considering the investigated stiffness distribution ratio.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• 제24권2호
• /
• pp.102-110
• /
• 2012

The objective of this study is to improve the performance of a hybrid ground source heat pump (HGSHP) by optimizing the flow distribution ratio of secondary fluid flow rate between a ground loop and a supplemental loop. Initially, a conventional ground source heat pump (GSHP) was tested to determine an optimum flow rate of the secondary fluid. Based on the selected optimum value, the HGSHP was also tested by varying the flow distribution ratio of the secondary fluid flow rate between the ground loop and the supplemental loop, such as 9:1, 7:3, 5:5, and 3:7. The results showed that the optimum flow distribution ratio of the secondary fluid flow rate was 7:3. The COP of the HGSHP was improved by 19% over the GSHP at a flow distribution ratio of 7:3 and an entering water temperature of $40^{\circ}C$.

• Journal of the Korean Data and Information Science Society
• /
• 제20권3호
• /
• pp.587-592
• /
• 2009

The most frequent use of the chi-square distribution is in the area of goodness-of-t of a distribution. The likelihood ratio test is a commonly used test statistic as the maximum likelihood estimate in statistical inferences. The recently revised versions of the likelihood ratio test statistics are used in estimating the parameter in the chi-square distribution. The estimates are compared with the commonly used method of moments and the maximum likelihood estimate.

• KCI Concrete Journal
• /
• 제12권1호
• /
• pp.131-138
• /
• 2000

The research purpose of this paper is to investigate the influential Parameters on the unbonded tendon stress. The parameters were the reinforcing ratio, the prestressing ratio, and the loading type. To this end. first, the influence of parameters were examined with twenty eight test results obtained from references. Then, an experimental study was carried out with nine specimens. Test variables were the reinforcing ratio and the prestressing ratio. Specimens were divided equally into three groups and each group had a different level of the reinforcing ratio. Each specimen within a group has a different level of the prestressing ratio. The investigation with previous and current tests revealed the followings; (1) the length of crack distribution zone does not have a close relation with the length of plastic hinge. (2) the prestressing ratio does not affect both the length of crack distribution and the length of plastic hinge, (3) the tendon stress variation is in reverse relation with the ratios of mild steels and tendons, (4) the loading type nay not affect significantly the length of crack distribution zone, (5) AASHTO LRFD Code equation and Moon/Lim's design equation predicted the test results well with some safety margins.