• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.05a
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• pp.1661-1662
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• 2006

Internet communication network quality characteristics are analyzed using Beta probability distribution. Beta probability distribution is chosen for the underlying probability distribution because it is an extremely flexible probability distribution used to model bounded random variables. Based on the fitted Beta probability distribution, a dataset regarding each network quality characteristic is summarized concisely.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1563-1575
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• 2018

In this paper, our central focus is upon gamma and beta q-distributions from a probabilistic viewpoint. The gamma and the beta q-distributions are characterized by investing the nature of the joint q-probability density function through the q-independence property and the q-Laplace transform.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1069-1074
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• 2008

Tool condition monitoring (TCM) is crucial for improvement of productivity in manufacturing process. However, TCM techniques have not been applied to monitor tool failure in an industrial gear shaving application. Therefore, this work studied a statistical TCM method for monitoring gear shaving tool condition. The method modeled the shaving process using beta probability distribution in order to extract the effective features. Modeling includes rectifying for converting a bi-modal distribution into a unimodal distribution, estimating parameters of beta probability distribution based on method of moments. The usefulness of features obtained from the proposed method was evaluated and discussed.

• 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 Institute of Control, Robotics and Systems
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• v.20 no.8
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• pp.854-867
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• 2014

This paper deals with the performance comparison of a PSO algorithm inspired in the process of simulating the behavior pattern of the organisms. The PSO algorithm finds the optimal solution (fitness value) of the objective function based on a stochastic process. Generally, the stochastic process, a random function, is used with the expression related to the velocity included in the PSO algorithm. In this case, the random function of the normal distribution (Gaussian) or uniform distribution are mainly used as the random function in a PSO algorithm. However, in this paper, because the probability distribution which is various with 2 shape parameters can be expressed, the performance comparison of a PSO algorithm using the beta probability distribution function, that is a random function which has a high degree of freedom, is introduced. For performance comparison, 3 functions (Rastrigin, Rosenbrock, Schwefel) were selected among the benchmark Set. And the convergence property was compared and analyzed using PSO-FIW to find the optimal solution.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.451-456
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• 2005

We introduce the standard two-sided power normal distribution and consider the relation between the probability in standard two-sided power distribution and the probability in standard two-sided power normal distribution and obtain the even moment of the special two-sided power normal distribution including the cases considered by Gupta and Nadarajah(2004)

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.441-446
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• 2003

Let { $X_{n}$ , n $\geq$ 1} be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function f(x). Let $Y_{n}$ = max{ $X_1$, $X_2$, …, $X_{n}$ } for n $\geq$ 1. We say $X_{j}$ is an upper record value of { $X_{n}$ , n$\geq$1} if $Y_{j}$ > $Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, n$\geq$1, where u(n) = min{j｜j>u(n-1), $X_{j}$ > $X_{u}$ (n-1), n$\geq$2} and u(1) = 1. We call the random variable X $\in$ Beta (1, c) if the corresponding probability cumulative function F(x) of x is of the form F(x) = 1-(1-x)$^{c}$ , c>0, 0$\leq$x$\leq$1. In this paper, we will give a characterization of the beta distribution of the first kind by considering conditional expectations of record values.s.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.379-389
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• 2002

For two normal distribution with unknown means and unknown variances, a sequential procedure for estimating the difference of two normal means which satisfies both the coverage probability condition and the $\beta$-protection is proposed under some smoothness of variable imprecision function, and the asymptotic normality of the proposed stopping time after some centering and scaling is given.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.1
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• pp.11-18
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• 2010

Tool condition monitoring (TCM) is crucial for improvement of productivity in manufacturing process. However, TCM techniques have not been applied to monitor tool failure in an industrial gear shaving application. Therefore, this work studied a statistical TCM method for monitoring gear shaving tool condition. The method modeled the vibration signal of the shaving process using beta probability distribution in order to extract the effective features for TCM. Modeling includes rectifying for converting a bi-modal distribution into a unimodal distribution, estimating the parameters of beta probability distribution based on method of moments. The performance of features obtained from the proposed method was evaluated and discussed.

• Journal of Ocean Engineering and Technology
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• v.18 no.2
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• pp.64-69
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• 2004

The characteristics of the probability distribution for mechanical properties, e.g. tensile strength, reduction of area, and elongation, for STS304 stainless steel in elevated temperature are investigated. Tensile test is performed by constant crosshead speed controls with 1mm/min. The probability distribution function of measured mechanical properties seems to follow $\alpha$ 3-parameter Weibull, and shows a slight dependence on the temperature. When the temperature is raised, the shape parameter a is increased, but both the scale parameter $\beta$ and location parameter v are decreased.