• Journal of applied mathematics & informatics
• /
• v.42 no.3
• /
• pp.709-723
• /
• 2024

We study the distributions of waiting times in variations of the geometric distribution of order k. Variation imposes length on the runs of successes and failures. We study two types of waiting time random variables. First, we consider the waiting time for a run of k consecutive successes the first time no sequence of consecutive k failures occurs prior, denoted by T^(k). Next, we consider the waiting time for a run of k consecutive failures the first time no sequence of k consecutive successes occurred prior, denoted by J^(k). In addition, we study the distribution of the weighted average. The exact formulae of the probability mass function, mean, and variance of distributions are also obtained.

• Journal of the Korean Data and Information Science Society
• /
• v.24 no.6
• /
• pp.1449-1454
• /
• 2013

There are many methods for measuring the difference between two location parameters. In this paper, statistics are proposed in order to estimate the difference of two location parameters. The statistics are designed not using the means, variances, signs and ranks, but with the cumulative distribution functions. Hence these are measured as the differences in the area between two univariate cumulative distribution functions. It is found that the difference in the area between two empirical cumulative distribution functions is the difference of two sample means, and its integral is also the difference of two population means.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.44 no.4
• /
• pp.220-226
• /
• 2021

In supply chain, there are a variety of different uncertainties including demand, service time, lead time, and so forth. The uncertainty of demand has been commonly studied by researchers or practitioners in the field of supply chain. However, the uncertainty of upstream supply chain has also increased. A problem of uncertainty in the upstream supply chain is the fluctuation of the lead time. The stochastic lead time sometimes causes to happen so called the order crossover which is not the same sequences of the order placed and the order arrived. When the order crossover happens, ordinary inventory policies have difficult to find the optimal inventory solutions. In this research, we investigate the lead time distribution in case of the order crossover and explore the resolutions of the inventory solution with the order crossover.

• Communications for Statistical Applications and Methods
• /
• v.21 no.2
• /
• pp.147-160
• /
• 2014

In this paper, we introduce the exponentiated Weibull-geometric (EWG) distribution which generalizes two-parameter exponentiated Weibull (EW) distribution introduced by Mudholkar et al. (1995). This proposed distribution is obtained by compounding the exponentiated Weibull with geometric distribution. We derive its cumulative distribution function (CDF), hazard function and the density of the order statistics and calculate expressions for its moments and the moments of the order statistics. The hazard function of the EWG distribution can be decreasing, increasing or bathtub-shaped among others. Also, we give expressions for the Renyi and Shannon entropies. The maximum likelihood estimation is obtained by using EM-algorithm (Dempster et al., 1977; McLachlan and Krishnan, 1997). We can obtain the Bayesian estimation by using Gibbs sampler with Metropolis-Hastings algorithm. Also, we give application with real data set to show the flexibility of the EWG distribution. Finally, summary and discussion are mentioned.

• Journal of applied mathematics & informatics
• /
• v.41 no.5
• /
• pp.1047-1056
• /
• 2023

This article studies some moments characteristics of generalized order statistics for transmuted power hazard distribution. It unifies the earlier results considered by several authors. The characterization results are also outlined at the end.

• The Journal of Korean Physical Therapy
• /
• v.17 no.4
• /
• pp.505-517
• /
• 2005

The Purposes of this study were to find complementary connectible new factors that analyzed correlation relate of Sasang Constitution and GCM Body Type in Static Posture and Dynamic Hyper/Hypo-mobility Pattern. Method of this study was asymtomatic volunteers 232(unmarried man and women), conducted from September 1 to December 31. In this main study progressing step diagnosised first, Constitution of Sasang medicine after being classified into four groups of Soyangin, Taeumin, Soeumin, Taeyangin diagnosis of GCM Body Type and progressed that related Static Posture and Dynamic Hyper/Hypo mobility Pattern. The results are as follows. Distribution of Sasang Medicine Constitution proved to be Taeyangin 13, Soyangin 66, Taeumin 67, Soeumin 86 respectively. Distribution of GCM Body Type proved I Body Type 72(31.0%), II Body Type 54(23.3%), III Body Type 89(38.4%), IV Body Type 17(7.3%). The distribution of Sasang Constitution according to GCM Body Type was that; I Body Type was distributed in the order Soeumin 34.7%(25), Taeumin 31.9%(23), Soyangin 30.6%(22), Soeumin 34.7%(25) is the most people. II Body Type was distribution of in the order Soeumin 42.6%(23), Soyangin 5.9%(14), Taeumin 24.1%(13), Soeumin 42.6%(23) is the most people. III Body Type was distribution of in the order Soeumin 37.1%(33), Taeumin 30.3%(27), Soyangin 28.1%(25), Soeumin 37.1% is the most people. IV Body Type proved high distribution each of Soeumin 29.4%(5) and Soyangin 29.4%(5). In case of main left side posture character of spine and limbs about I Body Type 72 persons with left scapular and ilium forward tilted pattern proved in the order high distribution iliac crest thigh and scapular high 70(97.2%), gluteal fold high and scapular abduction 69(95.8%), lumbar scoliosis 65(90.3%). Also, in case of right side posture character proved in the order high distribution deep gluteal fold 69(95.8%), umbilical deviation 68(94.4%). Incase of main left side posture character of spine and limbs about n Body Type 54 persons proved in the: order high distribution knee hyperextension 50(92.6%), shoulder deviation 49(90.7%) etc. Also, in case of right side posture character proved in the order high distribution pelvic deviation 53(98.1%), iliac crest thigh 52(96.3%), hip flexion and ankle inversion 51(94.4%) etc. In case of main left side posture character of spine and limbs about III Body Type 89 persons proved in the order high distribution shoulder deviation 87(97.8%), scapular abduction 86(96.6%), scapular high 85(95.5%) etc. And in case of right side posture character proved in the order high distribution pelvic deviation and iliac crest thigh 86(96.6%) etc. In case of main left side posture character of spine and limbs about IV Body Type 17 persons proved in the order high distribution pelvic deviation, lumbar sciliosis and lumbar lordosis increase 15(88.2%) etc. Also, in case of right side posture character proved in the order high distribution wrist dorsiflexion 16(94.1%), thickened achilles tendon etc.

• Journal of the military operations research society of Korea
• /
• v.9 no.2
• /
• pp.39-43
• /
• 1983

In this paper, we derive the likelihood function for the independent random order statistic whose underlying lifetime distribution is a two parameter Weibull form. For this purpose we first discuss the order statistic which represent a characteristic feature of most life and fatigue tests that they give rise to ordered observations. And, we describe the properties of the underlying Weibull model. The derived likelihood function is essential for establishing the statistical life test plans in the case of Weibull distribution using a likelihood ratio method.

• Proceedings of the KIEE Conference
• /
• 2005.11b
• /
• pp.258-260
• /
• 2005

Recently, it is focused on a methodology to estimate a order of precedence investment in distribution power system under competitive electricity market. This paper suggests methodology to evaluate the order as using a sensitivity of system interruption cost in distribution system regarding a failure rate of distribution components. In this paper, by using one of feeder in RBTS model, the order is assessed to compare valuation about sensitivity of interruption cost with valuation about sensitivity of estimated reliability indices. In conclusion, it is shown that results of precedence investment based on each methods are difference.

• Journal of Korean Society for Quality Management
• /
• v.31 no.1
• /
• pp.109-122
• /
• 2003

This paper presents a robust process capability index(PCI) based on the expected loss derived from the empirical distribution function(EDF). We propose the EDF expected loss in order to develop a PCI that does not depends on the underlying process distribution. The EDF expected loss depends only on the sample data, so the PCI based on it is robust and it does nor require complex calculations. The inverted normal loss function(INLF) is employed in order to overcome the drawback of the quadratic loss which may Increase unboundedly outside the specification limits. A comprehensive simulation study was performed under various process distributions, in order to compare the accuracy and the precision of the proposed PCI with those of the PCI based on the expected loss derived from the normal distribution. The proposed PCI turned out to be more accurate than the normal PCI in most cases, especially when the process distribution has high kurtosis or skewness. It is expected that the proposed PCI can be utilized In real processes where the true distribution family may not be known.

• Journal of Korea Multimedia Society
• /
• v.17 no.3
• /
• pp.294-299
• /
• 2014

In this paper, we propose a novel algorithm to improve the performance of a voice activity detection(VAD) which is based on the generalized normal-Laplace(GNL) distribution. In our algorithm, the probability density function(PDF) of the noisy speech signal is represented by the GNL distribution and the variance of the speech and noise of GNL distribution are estimated using higher order moments. Experimental results show that the proposed algorithm yields better results compared to the conventional VAD algorithms.