• Journal of the Korea Society of Computer and Information
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• v.15 no.5
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• pp.125-132
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• 2010

Decision problem called an optimal release policies, after testing a software system in development phase and transfer it to the user, is studied. The applied model of release time exploited infinite non-homogeneous Poisson process. This infinite non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The failure life-cycle distribution used exponential and non-exponential family which has various intensity. Thus, software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.743-758
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• 2005

This paper consider penalized likelihood regression with data from exponential family. The fast computation method applied to Gaussian data(Kim and Gu, 2004) is extended to non Gaussian data through asymptotically efficient low dimensional approximations and corresponding algorithm is proposed. Also smoothing parameter selection is explored for various exponential families, which extends the existing cross validation method of Xiang and Wahba evaluated only with Bernoulli data.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1033-1047
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• 2009

In this paper, we consider a m-type risk model with Markov-modulated premium rate. A integral equation for the conditional ruin probability is obtained. A recursive inequality for the ruin probability with the stationary initial distribution and the upper bound for the ruin probability with no initial reserve are given. A system of Laplace transforms of non-ruin probabilities, given the initial environment state, is established from a system of integro-differential equations. In the two-state model, explicit formulas for non-ruin probabilities are obtained when the initial reserve is zero or when both claim size distributions belong to the $K_n$-family, n $\in$ $N^+$ One example is given with claim sizes that have exponential distributions.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1033-1043
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• 2011

In this paper, we use a nested family of models of Generalized Autoregressive Conditional Heteroscedasticity(GARCH) to verify asymmetric conditional heteroscedasticity in the KOSPI and Won-Dollar exchange rate. This study starts from an investigation of whether time series data have asymmetric features not explained by standard GARCH models. First, we use kernel density plot to show the non-normality and asymmetry in data as well as to capture asymmetric conditional heteroscedasticity. Later, we use three representative asymmetric heteroscedastic models, EGARCH(Exponential Garch), GJR-GARCH(Glosten, Jagannathan and Runkle), APARCH(Asymmetric Power Arch) that are improved from standard GARCH models to give a better explanation of asymmetry. Thereby we highlight the fact that volatility tends to respond asymmetrically according to positive and/or negative values of past changes referred to as the leverage effect. Furthermore, it is verified that how the direction of asymmetry is different depending on characteristics of time series data. For the KOSPI and Korean won-US dollar exchange rate, asymmetric heteroscedastic model analysis successfully reveal the leverage effect. We obtained predictive values of conditional volatility and its prediction standard errors by using moving block bootstrap.

• Radiation Oncology Journal
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• v.21 no.3
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• pp.227-237
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• 2003

Purpose: The human chronic myelogenous leukemia cell line, K562, expresses the chimeric bcr-abl oncoprotein, whose deregulated protein tyrosine kinase activity antagonizes via DNA damaging agents. Previous experiments have shown that nanomolar concentrations of herbimycin A (HWA) coupled with X-irradiation have a synergistic effect in inducing apoptosis in the Ph-positive K562 leukemia cell line, but genistein, a PTK inhibitor, is non selective for the radiation-induced apoptosils on $p210^{bcr/abl}$ protected K562 cells. In these experiments, the cytoplasmic signal transduction pathways, the Induction on a number of transcription factors and the differential gene expression in this model were investigated. Materials and Methids: K562 cells in the exponential growth phase were used in this study. The cells were irradiated with 0.5-12 Gy, using a 6 Mev Linac (Clinac 1800, Varian, USA). Immediately after irradiation, the cells were treated with $0.25/muM$ of HMA and $25/muM$ of genistein, and the expressions and the activities of abl kinase, MAPK family, NF- kB, c-fos, c-myc, and thymidine kinase1 (TK1) were examined. The differential gene expressions induced by PTK inhibitors were also investigated. Results: The modulating effects of herbimycin A and genistein on the radiosensitivity of K562 cells were not related to the bcr-abl kinase activity. The signaling responses through the MAPK family of proteins, were not involved either in association with the radiation-induced apoptosis, which is accelerated by HMA, the expression of c-myc was increased. The combined treatment of genistein, with irradiation, enhanced NF- kB activity and the TK1 expression and activity. Conclusion: The effects of HMA and genistein on the radiosensitivity on the K562 cells were not related to the bcr-abl kinase activity in this study, another signaling pathway, besides the WAPK family responses to radiation to K562 cells, was found. Further evaluation using this model will provide valuable information for the optional radiosensitization or radioprotection.