• Title/Summary/Keyword: Levy distribution

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Pharmacokinetics of Tobramycin in Patients with Hematologic Malignancy (혈액암 환자에 있어서의 Tobramycin Pharmacokinetics)

  • Yeom, Mikyong;Shin, Wan-Gyoon;Lee, Min-Hwa
    • Korean Journal of Clinical Pharmacy
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    • v.1 no.1
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    • pp.31-36
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    • 1991
  • Tobramycin is one of the most frequently selected agents for pharmacokinetic drug monitoring because of its narrow therapeutic index and essential role for the management of serious infections, especially gram-negative infections. Its pharmacokinetic parameters are dependent on race, sex, age, ideal body weight. disease states, and etc. Therefore, to schedule the dosing of tobramycin, the individual pharmacokinetic parameters such as half-life and volume of distribution are needed. However, these pharmacokinetic parameters have never been reported in Koreans. The purposes of this study were to evaluate the volume of distribution of tobramycin in cancer patients who had normal renal function, to compare the mean values of Vd reported in the literature, and to compare the measured half-life with the expected half-life based on ABW, LBW, and IBW, respectively. Venous blood samples were collected just before and thirty minutes after dosing during steady state. Serum tobramycin concentrations were determined by $TD_x$ (fluorescence immunoassay). IBW were measured by the method of Devine: and LBW were measured by the method of Hallynck. Creatinine clearances (CLcr) of the patients were estimated using the Cockcroft and Gault equation. Elimination rate constants (kel) were determined using the Welling and Craig equation. Infusion rate (ko), volume of distribution (Vd), and half-life $(t_{1/2})$ were determined using the Saw chuk and Zaske equation. The volume of distribution Was $27\%$ greater than the Schentag's study (0.26 vs 0.33 l/kg), but the half-life was similar to the Levy's study. The predicted half-lives based on IBW were the closest to actual half-lives (1.85 vs 2.01 hr).

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ON CONSISTENCY OF SOME NONPARAMETRIC BAYES ESTIMATORS WITH RESPECT TO A BETA PROCESS BASED ON INCOMPLETE DATA

  • Hong, Jee-Chang;Jung, In-Ha
    • The Pure and Applied Mathematics
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    • v.5 no.2
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    • pp.123-132
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    • 1998
  • Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

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Multifractal Stochastic Processes and Stock Prices (다중프랙탈 확률과정과 주가형성)

  • Rhee, Il-King
    • The Korean Journal of Financial Management
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    • v.20 no.2
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    • pp.95-126
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    • 2003
  • This paper introduces multifractal processes and presents the empirical investigation of the multifractal asset pricing. The multifractal stock price process contains long-tails which focus on Levy-Stable distributions. The process also contains long-dependence, which is the characteristic feature of fractional Brownian motion. Multifractality introduces a new source of heterogeneity through time-varying local reqularity in the price path. This paper investigates multifractality in stock prices. After finding evidence of multifractal scaling, the multifractal spectrum is estimated via the Legendre transform. The distinguishing feature of the multifractal process is multiscaling of the return distribution's moments under time-resealing. More intensive study is required of estimation techniques and inference procedures.

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Numerical studies on approximate option prices (근사적 옵션 가격의 수치적 비교)

  • Yoon, Jeongyoen;Seung, Jisu;Song, Seongjoo
    • The Korean Journal of Applied Statistics
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    • v.30 no.2
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    • pp.243-257
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    • 2017
  • In this paper, we compare several methods to approximate option prices: Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method using normal inverse gaussian (NIG) distribution, and an asymptotic method using nonlinear regression. We used two different types of approximation. The first (called the RNM method) approximates the risk neutral probability density function of the log return of the underlying asset and computes the option price. The second (called the OPTIM method) finds the approximate option pricing formula and then estimates parameters to compute the option price. For simulation experiments, we generated underlying asset data from the Heston model and NIG model, a well-known stochastic volatility model and a well-known Levy model, respectively. We also applied the above approximating methods to the KOSPI200 call option price as a real data application. We then found that the OPTIM method shows better performance on average than the RNM method. Among the OPTIM, A-type Gram-Charlier expansion and the asymptotic method that uses nonlinear regression showed relatively better performance; in addition, among RNM, the method of using NIG distribution was relatively better than others.

Option Pricing Models with Drift and Jumps under L$\acute{e}$vy processes : Beyond the Gerber-Shiu Model (L$\acute{e}$vy과정 하에서 추세와 도약이 있는 경우 옵션가격결정모형 : Gerber-Shiu 모형을 중심으로)

  • Cho, Seung-Mo;Lee, Phil-Sang
    • The Korean Journal of Financial Management
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    • v.24 no.4
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    • pp.1-43
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    • 2007
  • The traditional Black-Scholes model for option pricing is based on the assumption that the log-return of the underlying asset follows a Brownian motion. But this assumption has been criticized for being unrealistic. Thus, for the last 20 years, many attempts have been made to adopt different stochastic processes to derive new option pricing models. The option pricing models based on L$\acute{e}$vy processes are being actively studied originating from the Gerber-Shiu model driven by H. U. Gerber and E. S. W. Shiu in 1994. In 2004, G. H. L. Cheang derived an option pricing model under multiple L$\acute{e}$vy processes, enabling us to adopt drift and jumps to the Gerber-Shiu model, while Gerber and Shiu derived their model under one L$\acute{e}$vy process. We derive the Gerber-Shiu model which includes drift and jumps under L$\acute{e}$vy processes. By adopting a Gamma distribution, we expand the Heston model which was driven in 1993 to include jumps. Then, using KOSPI200 index option data, we analyze the price-fitting performance of our model compared to that of the Black-Scholes model. It shows that our model shows a better price-fitting performance.

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The Economic Effects of Tax Incentives for Housing Owners: An Overview and Policy Implications (주택소유자(住宅所有者)에 대한 조세감면(租稅減免)의 경제적(經濟的) 효과(效果) : 기존연구(旣存硏究)의 개관(槪觀) 및 정책시사점(政策示唆點))

  • Kim, Myong-sook
    • KDI Journal of Economic Policy
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    • v.12 no.2
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    • pp.135-149
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    • 1990
  • Housing owners in Korea have a variety of tax advantages such as income tax exemption for the imputed rent of owner-occupied housing, exemption from the capital gains tax and deduction of the estate tax for one-house households. These tax reliefs for housing owners not only conflict with the principle of horizontal and vertical equity, but also lead to resource misallocation by distorting the housing market, and thus bring about regressive distribution effects. Particularly in the case of Korea with its imperfect capital market, these measures exacerbate the inter-class inequality of housing ownership as well as inequalities in wealth, by causing the affluent to demand needlessly large housing, while the poor and young experience difficulties in purchasing residential properties. Therefore, the Korean tax system must be altered as follows in order to disadvantage owner-occupiers, especially those owners of luxury housing. These alterations will promote housing-ownership, tax burden equity, efficiency of resource allocation, as well as the desirable distribution of income. First, income tax deductions for the rent payments of tenants are recommended. Ideally, the way of recovering the fiscal equivalence between the owner-occupiers and tenants is to levy an income tax on the former's imputed rents, and if necessary to give them tax credits. This, however, would be very difficult from a practical viewpoint, because the general public may perceive the concept of "imputed rent" as cumbersome. Computing the imputed rent also entails administrative costs, rendering quite reasonable, the continued exemption of imputed rent from taxation with the simultaneous deduction in the income tax for tenants. This would further enhance the administrative efficiency of income tax collection by easing assessment of the landlord's income. Second, a capital gains tax should be levied on the one-house household, except with the postponement of payments in the case that the seller purchases higher priced property. Exemption of the capital gains tax for the one-house household favors those who have more expensive housing, providing an incentive to the rich to hold even larger residences, and to the constructors to build more luxurious housing to meet the demand. So it is not desirable to sustain the current one-house household exemption while merely supplementing it with fastidious measures. Rather, the rule must be abolished completely with the concurrent reform of the deduction system and lowering of the tax rate, measures which the author believes will help optimize the capital gains tax incidence. Finally, discontinuation of the housing exemption for the heir is suggested. Consequent increases in the tax burden of the middle class could be mitigated by a reduction in the rate. This applies to the following specific exemptions as well, namely, for farm lands, meadows, woods, business fields-to foster horizontal equity, while denying speculation on land that leads to a loss in allocative efficiency. Moreover, imperfections in the Korean capital market have disallowed the provision of long term credit for housing seekers. Remedying these problems is essential to the promotion of greater housing ownership by the low and middle income classes. It is also certain that a government subsidy be focused on the poorest of the poor who cannot afford even to think of owning a housing.

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