• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.473-495
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• 2019

In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. A modified goodness-of-fit test using the Nikulin-Rao-Robson statistic test is investigated via two examples and is observed that the new extension might be used as an alternative lifetime model.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.215-223
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• 1996

By using Tukey's generalized lambda distribution, appoximate posterior density is derived under the Bayes-empirical Bayes model. The sensitivity of posterior distribution to the hyperprior distribution is examined by using Tukey's generalized lambda distriburion which approximate many well-knmown distributions. Based upon Monte Varlo simulation studies it can be said that posterior distribution is sensitive to the cariance of the prior distribution and to the symmetry of the hyperprior distribution. Also posterior distribution is approximately obtained by using the following methods : Lindley method, Laplace method and Gibbs sampler method.

• Journal of Integrative Natural Science
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• v.5 no.3
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• pp.186-189
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• 2012

For the mean vector of a p-variate normal distribution ($p{\geq}3$), the optimal estimation within the class of James-Stein type decision rules under the quadratic loss are given when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}\underline{{\theta}}{\parallel}$ in known. It also demonstrated that the optimal estimation within the class of Lindley type decision rules under the same loss when the underlying distribution is the previous type and the norm ${\parallel}{\theta}-\overline{\theta}\underline{1}{\parallel}$ with $\overline{\theta}=\frac{1}{p}\sum\limits_{i=1}^{n}{\theta}_i$ and $\underline{1}=(1,{\cdots},1)^{\prime}$ is known.

• Communications for Statistical Applications and Methods
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• v.20 no.5
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• pp.405-416
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• 2013

This paper develops a maximum profile likelihood estimator of unknown parameters of the exponentiated Gumbel distribution based on upper record values. We propose an approximate maximum profile likelihood estimator for a scale parameter. In addition, we derive Bayes estimators of unknown parameters of the exponentiated Gumbel distribution using Lindley's approximation under symmetric and asymmetric loss functions. We assess the validity of the proposed method by using real data and compare these estimators based on estimated risk through a Monte Carlo simulation.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1573-1582
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• 2015

In lifetime data analysis, it is generally known that the lifetimes of test items may not be recorded exactly. There are also situations wherein the withdrawal of items prior to failure is prearranged in order to decrease the time or cost associated with experience. Moreover, it is generally known that more than one cause or risk factor may be present at the same time. Therefore, analysis of censored competing risks data are needed. In this article, we derive the Bayes estimators for the entropy function under the exponential distribution with an unknown scale parameter based on multiply Type II censored competing risks data. The Bayes estimators of entropy function for the exponential distribution with multiply Type II censored competing risks data under the squared error loss function (SELF), precautionary loss function (PLF) and DeGroot loss function (DLF) are provided. Lindley's approximate method is used to compute these estimators.We compare the proposed Bayes estimators in the sense of the mean squared error (MSE) for various multiply Type II censored competing risks data. Finally, a real data set has been analyzed for illustrative purposes.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.10 no.5
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• pp.469-475
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• 2017

Software reliability is one of the most basic and essential problems in software development. In order to detect the software failure phenomenon, the intensity function, which is the instantaneous failure rate in the non-homogeneous Poisson process, can have the property that it is constant, non-increasing or non-decreasing independently at the failure time. In this study, was compared the reliability performance of the software reliability model using the Landely lifetime distribution with the intensity function decreasing pattern and Erlang lifetime distribution from increasing to decreasing pattern in the software product testing process. In order to identify the software failure phenomenon, the parametric estimation was applied to the maximum likelihood estimation method. Therefore, in this paper, was compared and evaluated software reliability using software failure interval time data. As a result, the reliability of the Landely model is higher than that of the Erlang distribution model. But, in the Erlang distribution model, the higher the shape parameter, the higher the reliability. Through this study, the software design department will be able to help the software design by applying various life distribution and shape parameters, and providing software reliability attributes data and basic knowledge to software reliability model using software failure analysis.

• Journal of Korean Society of Forest Science
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• v.62 no.1
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• pp.24-42
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• 1983

To develop Ilex cornuta which grow naturally in the southwest seaside district as new ornamental tree, the author chose I. cornuta growing in the four natural communities and those cultivated in Kwangju city as a sample, and investigated its ecology, morphology and characteristics. The results obtained was summarized as follows; 1) The natural distribution of I. cornuta marks $35^{\circ}$43'N and $126^{\circ}$44'E in the southwestern part of Korea and $33^{\circ}$20'N and $126^{\circ}$15'E in Jejoo island. This area has the following necessary conditions for Ilex cornuta: the annual average temperature is above $12^{\circ}C$, the coldness index below $-12.7^{\circ}C$, annual average relative humidity 75-80%, and the number of snow-covering days is 20-25 days, situated within 20km of from coastline and within, 100m above sea level and mainly at the foot of the mountain facing the southeast. 2) The vegetation in I. cornuta community can be divided that upper layer is composed of Pinus thunbergii and P. densiflora, middle layer of Eurya japonica var. montana, Ilex cornuta and Vaccinium bracteatum, and the ground vegetation is composed of Carex lanceolata and Arundinella hirta var. ciliare. The community has high species diversity which indicates it is at the stage of development. Although I. cornuta is a species of the southern type of temperate zone where coniferous tree or broad leaved, evergreen trees grow together, it occasionally grows in the subtropical zone. 3) Parent rock is gneiss or rhyolite etc., and soil is acidic (about pH 4.5-5.0) and the content of available phosphorus is low. 4) At maturity, the height growth averaged $10.48{\pm}0.23cm$ a year and the diameter growth 0.43 cm a year, and the annual ring was not clear. Mean leaf-number was 11.34. There are a significant positive correlation between twig-elongation and leaf-number. 5) One-year-old seedling grows up to 10.66 cm (max. 18.2 cm, min. 4.0 cm) in shoot-height, with its leaf number 12.1 (max. 18, min), its basal diameter 2.24 mm (max. 4.0 mm, min. 1.0 mm) and shows rhythmical growth in high temperature period. There were significant positive correlations between stalk-height and leaf-number, between stalk-height and basal-diameter, and between number and basal diameter. 6) The flowering time ranged from the end of April to the beginning of May, and the flower has tetra-merouscorella and corymb of yellowish green. It has a bisexual flower and dioecism with a sexual ratio 1:1. 7) The fruit, after fertilization, grows 0.87 cm long (0.61-1.31 cm) and 0.8 cm wide (0.62-1.05 cm) by the beginning of May. Fruits begin to turn red and continue to ripen until the end of October or the beginning of November and remain unfading until the end of following May. With the partial change in color of dark-brown at the beginning of the June fruits begin to fall, bur some remain even after three years. 8) The seed acquision ratio is 24.7% by weight, and the number of grains per fruit averages 3.9 and the seed weight per liter is 114.2 gram, while the average weight of 1,000 seeds is 24.56 grams. 9) Seeds after complete removal of sarcocarp, were buried under ground in a fixed temperature and humidity and they began to develop root in October, a year later and germinated in the next April. Under sunlight or drought, however, the dormant state may be continued.

• Journal of Korean Society of Forest Science
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• v.42 no.1
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• pp.1-38
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• 1979

The woody species of Genus Ilex which are endemic to Korea are distributed on limited area due to solely temperature factor. There is some differences according to species, however in general, the evergreen Ilex are found along southern coastal area of Korean Peninsula and near islands where the cold index does not exceed $-5^{\circ}C$. But Ilex macropoda and the variety, only deciduous ones, are grown in temperate zone of the peninsula and some islands. The list of Ilex species of Korea are as follows. Ilex cornuta Lindley et Pax., I. crenata Thunb. var. microphylla Max., I. crenata Thunb., I. rotunda Thunb., I. macropoda Miq., I. macropoda Miq. var. pseudo-macropoda Loensner, I. integra Thunb. The author surveyed the populations of Ilex species as many as possible and data of some characters such as leaf shape, spine, fruit shape, stomata density, sex ratio in natural communities, etc. are collected. Almost all the Ilex species in Korea show sporadic distribution. This means quite small sized populations isolate distantly each other eliminating the change of gene exchange in between. Particularly Ilex conuta and I. crenata show the morphological differentiation among populations as well as significant individual variation within a population. These were true with such characteristics, leaf shape, leaf dimension, leaf margin, fruit shape, spine, and stomata density. The founded are that the fruit length and the stomata density counted on the beneath surface of leaves of Ilex cornuta increased with the decrease of latitude. These are naturally closely related with the cold index values. The table shown below indicates the correlation between mean stomata density per $0.3642mm^2$ and cold index values. These relation however were not observed on Ilex crenata. The most dominated natured in relation to individual variation were outline of leaf, the number of marginal spine, the shape of leaf cross section and the degree of luster of the upper leaf surface. As shown in photos 5~7, these variations are agreed at a glance. There are reports that the development of marginal spines in some Ilex species is associated with the juvenility and topophysis. In present study, these two factors were neglected because of the intended sampling procedure. Of Ilex rotunda, population difference with the characteristics of leaf length is recognized but not for leaf width, petiole length, and fruit size. However, individual variations within a population were significantly large. In case of Ilex integra, only individual differences within population were calculated statistically for such characteristics as leaf length, leaf width, and petiole length. As to natural population, the sex ratio was 1:2 (female to male) for Ilex cornuta, and 1:1 for Ilex crenata. The tendency of more male than female in I. cornuta was agreed to other observations. Preparing the tip cutting of length 10cm, and treating with IBA, then attaching earth ball to the cut end, very successful rooting percentages were obtained. Asexual propagation has the advantages of maintaining the heterozygosity of existing varieties and overcoming the difficulties of delayed seed germination frequently encountered with Ilex species. Considering a great deal of variation in morphological traits, a good possibility of selection breeding for decorative and ornamental purposes exists. At present, these evergreen Ilex are ignored by local people as nuisance weedy shrubs. So the proper protection measures should promptly be taken.