• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.353-365
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• 2017

In this article, we proposed a new three-parameter distribution called generalized half-logistic Poisson distribution with a failure rate function that can be increasing, decreasing or upside-down bathtub-shaped depending on its parameters. The new model extends the half-logistic Poisson distribution and has exponentiated half-logistic as its limiting distribution. A comprehensive mathematical and statistical treatment of the new distribution is provided. We provide an explicit expression for the $r^{th}$ moment, moment generating function, Shannon entropy and $R{\acute{e}}nyi$ entropy. The model parameter estimation was conducted via a maximum likelihood method; in addition, the existence and uniqueness of maximum likelihood estimations are analyzed under potential conditions. Finally, an application of the new distribution to a real dataset shows the flexibility and potentiality of the proposed distribution.

• Journal of Integrative Natural Science
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• v.7 no.2
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• pp.138-144
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• 2014

Fisher information matrix plays an important role in statistical inference of unknown parameters. Especially, it is used in objective Bayesian inference where we calculate the posterior distribution using a noninformative prior distribution, and also in an example of metric functions in geometry. To estimate parameters in a distribution, we can use the Fisher information matrix. The more the number of parameters increases, the more its matrix form gets complicated. In this paper, by using Mathematica programs we derive the Fisher information matrix for 4-parameter generalized gamma distribution which is used in reliability theory.

• Magazine of the Korean Society of Agricultural Engineers
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• v.36 no.3
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• pp.122-134
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• 1994

The objective of this study is to provide with the hydrometeological and probabilistic characteristics of the storms and winds of typhoons that have been passed through the Korea peninsula during the last twenty-three years since 1961. The paths and intensities of the typhoons were analyzed. Fifty weather stations were selected and the rainfall and wind data during typhoon periods were collected. Rainfall data were analyzed for the patterns and probabilistic distributions. The results were presented to describe the areal distributions of probabilistic characteristics. Wind data were also analysed for their probabilistic distributions. The results obtained from this study can be summarized as follows: 1. The most frequent typhoon path that have passed through the Korean peninsula was type E, which was followed by types CWE, W, WE, and S. The most frequent typhoon intensity was type B, that was followed by A, super A, and C types, respectively. 2. The third quartile typhoon rainfall patterns appear most frequently followed by the second, first, and quartiles, respectively, in Seoul, Pusan, Taegu, Kwangju and Taejon. The single typhoon rainfalls with long rainfall durations tended to show delayed type rainfall patterns predominantly compared to the single rainfalls with short rainfall durations. 3. The most frequent probabilistic distribution for typhoon rainfall event is Pearson type-III, followed by Two-parameter lognormal distribution, and Type-I extremal distribution. 4. The most frequent probability distribution model of seashore location was Pearson type-III distribution. The most frequent probability distribution model of inland location was two parameter lognormal distribution. 5. The most frequent probabilistic distribution for typhoon wind events was Type-I xtremal distribution, followed by Two-parameter lognormal distribution, and Normal distribution.

• Water for future
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• v.29 no.4
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• pp.177-186
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• 1996

The analytical approach to determine transverse sand bed slope at river bend are based on two phases that the flow is considered as fully developed flow and the bed is fluvial having bed load. All existing methods are theoretically derived from the initiation of motion of the particles at river bed. They assume that the Shields parameter has a constant value of 0.06. In this study, the variability of Shields parameter due to the differences of shape of grain size distribution is considered. Therefore the parameter is not a constant, 0.06, but depends on the shape of the grain size distribution. This result gives good agreement to estimate transverse bed slope with actual field data at river bend.

• Journal of Digital Convergence
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• v.12 no.3
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• pp.219-226
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• 2014

In this study, reliability software cost model considering shape parameter based on life distribution from the process of software product testing was studied. The shape parameter using the Erlang and Log-logistic model that is widely used in the field of reliability problems presented. The software failure model was used finite failure non-homogeneous Poisson process model, the parameters estimation using maximum likelihood estimation was conducted. In comparison result of software cost model based on the Erlang distribution and the log-logistic distribution software cost model, because Erlang model is to predict the optimal release time can be software, but the log-logistic model to predict to optimal release time can not be, Erlang distribution than the log-logistic distribution appears to be effective. In this research, software developers to identify software development cost some extent be able to help is considered.

• Magazine of the Korean Society of Agricultural Engineers
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• v.21 no.4
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• pp.108-117
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• 1979

In order to obtain the basic data for design of water structures which can be contributed to the planning of water use. Best fitted distribution function and the equations for the probable minimum flow were derived to the annual minimum flow of five subwatersheds along Geum River basin. The result were analyzed and summarized as follows. 1. Type III extremal distribution was considered as a best fit one among some other distributions such as exponential and two parameter lognormal distribution by $x^2$-goodness of fit test. 2. The minimum flow are analyzed by Type III extremal distribution which contains a shape parameter $\lambda$, a location parameter ${\beta}$ and a minimum drought $\gamma$. If a minimum drought $\gamma=0$, equations for the probable minimum flow, $D_T$, were derived as $D_T={\beta}e^{\lambda}1^{y'}$, with two parameters and as $D_T=\gamma+(\^{\beta}-\gamma)e^{{\lambda}y'}$ with three parameters in case of a minimum drought ${\gamma}>0$ respectively. 3. Probable minimum flow following the return periods for each stations were also obtained by above mentioned equations. Frequency curves for each station are drawn in the text. 4. Mathematical equation with three parameters is more suitable one than that of two parameters if much difference exist between the maximum and the minimum value among observed data.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.393-402
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• 2014

The simplest and the most important distribution in survival analysis is the exponential distribution. In this paper, we investigate the influence of the random censorship model on the estimation of the scale parameter of the exponential distribution. The considered random censorship models are Koziol-Green model and the generalized exponential distribution model. Two models have different meanings. Through the simulation study, the averages of the estimated values of the parameter do not show big differences, however the MSE of the estimator tends to be bigger when the supposed model is significantly different from the true model.

• Journal of the Korean Data and Information Science Society
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• v.5 no.2
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• pp.19-27
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• 1994

It is known that the maximum likelihood method does not provide explicit estimator for the scale parameter of the Weibull distribution based on Type-II censored samples. In this paper we provide an approximate maximum likelihood estimator (AMLE) of the scale parameter of the Weibull distribution with Type-II censoring. We obtain the asymptotic variance and simulate the values of the bias and the variance of this estimator based on 3000 Monte Carlo runs for n = 10(10)30 and r,s = 0(1)4. We also simulate the absolute biases of the MLE and the proposed AMLE for complete samples. It is found that the absolute bias of the AMLE is smaller than the absolute bias of the MLE.

• Journal of Ocean Engineering and Technology
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• v.15 no.3
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• pp.20-27
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• 2001

After using the filtering method, wave parameters are calculated by the spectral analysis and wave by wave analysis. Extreme environments and higher wave characteristics int he Chujeon Sea are analyzed using the observed wave data. Higher wave has been intensely emphasized as an important environmental force parameter in several recent research works. The aims of this study are to summarize the distribution of extreme environment for wind waves, and to find occurrence probability of higher wave in Chujeon Sea. Ocean wave statistics varying with sea state are found to respond linearly to the spectral peakedness parameter Qp, mean run-length and Ursell number. Although the spreading of the field results is large, it may be concluded that the tendency of wave group formation depends on the spectral peakedness parameter Qp. Extreme wave is estimated to apply various model distribution functions by using the monthly maximum significant wave parameters which can be used to the design and analysis of coastal structures.

• Journal of the Korean Data and Information Science Society
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• v.19 no.3
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• pp.995-1006
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• 2008

This article deals with the one-sided hypothesis testing problem in inverse Gaussian distribution. We propose Bayesian hypothesis testing procedures for the one-sided hypotheses of the shape parameter under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the objective Bayesian hypothesis testing procedures based on the fractional Bayes factor, the median intrinsic Bayes factor and the encompassing intrinsic Bayes factor under the reference prior. Simulation study and a real data example are provided.