• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.1171-1177
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• 2007

We consider estimation of the right-tail probability in a log-Laplace random variable, As we derive the density of ratio of two independent log-Laplace random variables, the k-th moment of the ratio is represented by a special mathematical function. and hence variance of the ratio can be represented by a psi-function.

• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.1
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• pp.49-58
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• 1997

In this paper, a transfer function was obtained for a PWM high speed solenoid valve controlled metal belt CVT system. The transfer function was defined as the ratio of speed ratio to PWM duty ratio and derived in time domain by linear regression analysis from the experimental results. The transfer function obtained showed different dynamic characteristics for the up and down shift. Also, LQG/LTR controller was designed for the CVT system using the transfer function. It is seen from the experimental results that LQG/LTR control showed good performance for the speed ratio tracking and disturbance rejection. The phase difference and relatively slow response are considered due to the inaccuracy os the transfer functions, which resulted from the inherent nonlinearities of the transmission characteristics of the metal belt CVT.

• 한국디지털정책학회:학술대회논문집
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• 2006.12a
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• pp.327-336
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• 2006

The odds ratio is used for assessing the disease-exposure association, because epidemiological data for case-control of cohort studies are often summarized into 2 ${\times}$ 2 tables. In this paper we define the odds ratio function(ORF) that extends odds ratio used on discrete survival event data to continuous survival time data and propose estimation procedures with censored data. The first one is a nonparametric estimator based on the Nelson-Aalen estimator of comulative hazard function, and the others are obtained using the concept of empirical odds ratio. Asymptotic properties such as consistency and weak convergence results are also provided. The ORF provides a simple interpretation and is comparable to survival function or comulative hazard function in comparing two groups. The mean square errors are investigated via Monte Carlo simulation. The result are finally illustrated using the Melanoma data.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.117-121
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• 2016

In this paper we give a determinant formula for the ratio of relative congruence zeta functions of cyclotomic function fields.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-667
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• 2011

A class of functions involving divided differences of the psi and tri-gamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving the ratio of two gamma functions and originating from the establishment of the best upper and lower bounds in Kershaw's double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in $\mathbb{R}^{n-1}$ and $\mathbb{R}^n$ respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized.

• Journal of Biosystems Engineering
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• v.40 no.4
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• pp.314-319
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• 2015

Purpose: The ratio of straw to grain mass as a function of cutting height affects combine efficiency and power consumption and is an important input parameter to combine simulation models. An equation was developed to predict straw to grain ratios for wheat as a function of cutting height. Methods: Two mass functions, one for straw and one for grain, were developed using regression techniques and measured data collected in west Texas during the summer, and used to predict the straw to grain ratio. Results: Three equations were developed to facilitate the simulation of a combine during wheat harvest. Two mass functions, one for straw and one for grain, were also developed; a quadratic equation describes the straw mass with an $R^2$ of 0.992. An S-shaped curve describes the mass function for grain with an $R^2$ of 0.957. An equation for straw to grain ratio of wheat was developed as a function of cutting height. The straw to grain ratio has an $R^2$ value of 0.947. Conclusions: In all cases, the equations had $R^2$ values above 0.94 and were significant at the 99.9 percent probability level (alpha = 0.001). Although all three equations are useful, the grain mass and straw to grain ratio equations will have direct application in combine simulation models.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.541-547
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• 2009

We consider distribution, reliability and moment of ratio in two independent beta random variables X and Y, and reliability and $K^{th}$ moment of ratio are represented by a mathematical generalized hypergeometric function. We introduce an approximate maximum likelihood estimate(AML) of reliability and right-tail probability in the beta distribution.

• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1213-1222
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• 2012

We shall derive the moment of the ratio Y/(X + Y) and the reliability P(X < Y ), and then observe the skewness of the ratio in a bivariate Pareto density function of (X, Y). And we shall consider an approximate MLE of parameters in the bivariate Pareto density function.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.4
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• pp.953-959
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• 1998

To investigate accuracy of intensity method for measurement of the fiber orientation distribution, fiber orientation function is calculated by drawing simulation figures for the fiber orientation as varying fiber aspect ratio, fiber area ratio, and fiber orientation state, respectively. The values of fiber orientation function measured by intensity method are compared with the calculated values of fiber orientation function. The results show that measurement accuracy of the fiber orientation angle distribution by intensity method is affected by the fiber aspect ratio when the total length of oriented fiber is same. The average gradient of fiber orientation function is 0.94 for 1000mm of the total fiber length and is 0.93 for 2000 mm when the fiber aspect ratio is over 50. Measurement accuracy by intensity method is about 94% and the reliable data can be obtained by intensity method.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.955-960
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• 2009

As we shall dene an exponentiated complementary power function distribution, we shall consider moments, hazard rate, and inference for parameter in the distribution. And we shall consider an inference of the reliability and distributions for the quotient and the ratio in two independent exponentiated complementary power function random variables.