• International Journal of Reliability and Applications
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• v.16 no.2
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• pp.81-98
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• 2015

The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the $r^{th}$ moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1493-1510
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• 2000

Theoretical models that can be used to predict the range of main lobe widths and the probability distribution of the peak sidelobe levels of two-dimensionally sparse arrays are presented here. The arrays are considered to comprise microphones that are randomly positioned on a segmented grid of a given size. First, approximate expressions for the expected squared magnitude of the aperture smoothing function and the variance of the squared magnitude of the aperture smoothing function about this mean are formulated for the random arrays considered in the present study. By using the variance function, the mean value and the lower end of the range i.e., the first I percent of the mainlobe distribution can be predicted with reasonable accuracy. To predict the probability distribution of the peak sidelobe levels, distributions of levels are modeled by a Weibull distribution at each peak in the sidelobe region of the expected squared magnitude of the aperture smoothing function. The two parameters of the Weibull distribution are estimated from the means and variances of the levels at the corresponding locations. Next, the probability distribution of the peak sidelobe levels are assumed to be determined by a procedure in which the peak sidelobe level is determined as the maximum among a finite number of independent random sidelobe levels. It is found that the model obtained from the above approach predicts the probability density function of the peak sidelobe level distribution reasonably well for the various combinations of two different numbers of microphones and grid sizes tested in the present study. The application of these models to the design of random, sparse arrays having specified performance levels is also discussed.

• Journal of Navigation and Port Research
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• v.43 no.1
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• pp.1-8
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• 2019

Identifying behavioral errors of seafarers that have led to marine accidents is a basis for research into prevention or mitigation of marine accidents. The purpose of this study is to estimate the optimal probability distribution function needed to model behavioral errors of crew members into three behaviors (i.e., Skill-, Rule-, Knowledge-based). Through use of behavioral data obtained from previous accidents, we estimated the optimal probability distribution function for the three behavioral errors and verified the significance between the probability values derived from the probability distribution function. Maximum Likelihood Estimation (MLE) was applied to the probability distribution function estimation and variance analysis (ANOVA) used for the significance test. The obtained experimental results show that the probability distribution function with the smallest error can be estimated for each of the three behavioral errors for eight types of marine accidents. The statistical significance of the three behavioral errors for eight types of marine accidents calculated using the probability distribution function was observed. In addition, behavioral errors were also found to significantly affect marine accidents. The results of this study can be applied to predicting marine accidents caused by behavioral errors.

• International Journal of Reliability and Applications
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• v.1 no.2
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• pp.133-143
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• 2000

Data from weighted distributions appear, among other situations, when some of the data are missing or are damaged, a case that is important in reliability and life testing. The kernel method for hazard rate estimation is discussed for these data where the basic large sample properties are given. As a by product, the basic properties of the kernel estimate of the distribution function for data from weighted distribution are presented.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.547-562
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• 2005

The distribution of products of random variables is of interest in many areas of the sciences, engineering and medicine. This has increased the need to have available the widest possible range of statistical results on products of random variables. In this note, the distribution of the product | XY | is derived when X and Y are Student's t and Bessel function random variables distributed independently of each other.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.1-5
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• 2009

Let {$X_n,\;n{\geq}1}$ be a sequence of independent identically distributed(i.i.d.) sequence of positive random variables with common absolutely continuous distribution function(cdf) F(x) and probability density function(pdf) f(x) and $E(X^2)<{\infty}$. The random variables $\frac{X_i{\cdot}X_j}{(\Sigma^n_{k=1}X_k)^{2}}$ and $\Sigma^n_{k=1}X_k$ are independent for $1{\leq}i if and only if {$X_n,\;n{\geq}1}$ have gamma distribution.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.09a
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• pp.99-101
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• 2003

Unsaturated hydraulic conductivity models have been widely used for the numerical modeling of water flow and contaminant transport in soils. In this study, a simple hydraulic conductivity model is developed by using information of particle-size distribution from the lognormal distribution model and its results are compared with those from the Kosugi-Mualem (KM) model. The accuracy of the proposed model is verified for observed data chosen from the international UNSODA database. Results showed that the proposed model produces adequate predictions of hydraulic conductivities. Performance of this model is generally better than the KM function.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.261-265
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• 2017

Let X and Y be independent identically distributed nondegenerate random variables with common absolutely continuous probability distribution function F(x) and the corresponding probability density function f(x) and $E(X^2)$<${\infty}$. Put Z = max(X, Y) and W = min(X, Y). In this paper, it is proved that Z - W and Z + W or$(X-Y)^2$ and X + Y are independent if and only if X and Y have normal distribution.

• Journal of the Korean Statistical Society
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• v.19 no.2
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• pp.139-144
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• 1990

For the first-order bilinear time series model $X_t = aX_{t-1} + e_i + be_{t-1}X_{t-1}$ where ${e_i}$ is a sequence of independent normal random variables with mean 0 and variance $\sigma^2$, the asymptotic distribution of sample autocarrelation function is obtained and shown to follow a normal distribution. The variance of the asymptotic distribution is of a complicated form and hence a bootstrap estimate of the variance is proposed for large sample inference. This result can be used to distinguish between different bilinear models.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.363-374
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• 2006

A new bivariate beta distribution based on the Appell function of the third kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure as well as the Fisher information matrix.