• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.229-241
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• 1997

We consider discrimination curve and minimum dwell time for Poisson distribution and Poisson-power function distribution. Let the random variable X has Poisson distribution with mean .lambda.. For the hypothesis testing H$\_$0/:.lambda. = t vs. H$\_$1/:.lambda. = d (d$\_$0/ if X.leq.c. Since a critical value c can not be determined to satisfy both types of errors .alpha. and .beta., we considered discrimination curve that gives the maximum d such that it can be discriminated from t for a given .alpha. and .beta.. We also considered an algorithm to compute the minimum dwell time which is needed to discriminate at the given .alpha. and .beta. for the Poisson counts and proved its convergence property. For the Poisson-power function distribution, we reject H$\_$0/ if X.leq..'{c}.. Since a critical value .'{c}. can not be determined to satisfy both .alpha. and .beta., similar to the Poisson case we considered discrimination curve and computation algorithm to find the minimum dwell time for the Poisson-power function distribution. We prosent this algorithm and an example of computation. It is found that the minimum dwell time algorithm fails for the Poisson-power function distribution if the aiming error variance .sigma.$\^$2/$\_$2/ is too large relative to the variance .sigma.$\^$2/$\_$1/ of the Gaussian distribution of intensity. In other words, if .ell. is too small, we can not find the minimum dwell time for a given .alpha. and .beta..

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.279-285
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• 2008

This paper presents some characterizations of the Weibull distribution by the independence of record values. We prove that $X{\sim}Weibull(1,{\alpha})$, ${\alpha}>0$ if and only if $\frac{X_{U(n+1)}}{X_{U(n+1)}-X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent. We show that $X{\sim}Weibull(1,{\alpha})$, ${\alpha}>0$ if and only if $\frac{X_{U(n+1)}}{X_{U(n+1)}-X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent. And we establish that $X{\sim}Weibull(1,{\alpha})$, ${\alpha}>0$ if and only if $\frac{X_{U(n+1)}+X_{U(n)}}{X_{U(n+1)}-X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent.

• Journal of Pharmaceutical Investigation
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• v.17 no.4
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• pp.213-216
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• 1987

The distribution features of recombinant human $alpha-interferon(rHuIFN-{\alpha}A)$ and $^{14}C-radiolabeled\;rHuIFN-{\alpha}A\;(^{14}C-rHuIFN-{\alpha}A)$ were investigated in ICR mice after i.v. injection. The level of $rHuIFN-{\alpha}A$ in the kidney was significantly higher than those in lung and liver at 10min after the injection. But the level was reduced significantly at 60min. The level of radioactivity in the kidney was also significantly higher than those in other organs after i.v. injection of $^{14}C-rHuIFN-{\alpha}A$, but it was reduced at much slower speed than was $rHuIFN-{\alpha}A$. These results show that interferon is distributed repidly and the kidney is the main site of distribution and metabolism of $rHuIFN-{\alpha}A$.

• Computers and Concrete
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• v.11 no.5
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• pp.411-440
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• 2013

Large fluctuations in surface strain at the level of steel are expected in reinforced concrete flexural members at a given stage of loading due to the emergent structure (emergence of new crack patterns). This has been identified in developing deterministic constitutive models for finite element applications in Ibrahimbegovic et al. (2010). The aim of this paper is to identify a suitable probability distribution for describing the large deviations at far from equilibrium points due to emergent structures, based on phenomenological, thermodynamic and statistical considerations. Motivated by the investigations reported by Prigogine (1978) and Rubi (2008), distributions with heavy tails (namely, alpha-stable distributions) are proposed for modeling the variations in strain in reinforced concrete flexural members to account for the large fluctuations. The applicability of alpha-stable distributions at or in the neighborhood of far from equilibrium points is examined based on the results obtained from carefully planned experimental investigations, on seven reinforced concrete flexural members. It is found that alpha-stable distribution performs better than normal distribution for modeling the observed surface strains in reinforced concrete flexural members at these points.

• Korean Journal of Food Science and Technology
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• v.41 no.4
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• pp.369-373
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• 2009

${\alpha}$-Waxy corn starch was used as a feed for twin-screw extrusion in order to enhance starch liquefaction with added thermostable ${\alpha}$-amylase (derived from Bacillus licheniformis). The residence time distribution and starch liquefaction were investigated. The starch liquefaction was analyzed in terms of reducing sugar contents, molecular size from gel permeation chromatography (GPC), and microstructure from scanning electron microscopy (SEM). The use of ${\alpha}$-starch contributed to the production of more reducing sugar than the use of raw starch use alone. From GPC, the effect of ${\alpha}$- starch on the molecular size reduction was shown to be small. From SEM, irregular and damaged surface were observed on the extrudate from ${\alpha}$-starch, as compared to those from raw starch. The spread of residence time distribution curves was greater with feed of ${\alpha}$-starch than raw starch, indicating that ${\alpha}$-starch was hard to flow forward during extrusion. This could be improved by increasing the feed moisture content and barrel temperature of extruder.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.543-554
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• 1997

A family of some capability indices { $C_{p}$(.alpha.,.beta.); .alpha..geq.0, .beta..geq.0}, containing the indices $C_{p}$, $C_{{pk}}$, $C_{{pm}}$, and $C_{{pmk}}$, has been defined by Vannman(1993) for the case of two-sided specification interval. By varying the parameters of the family various capability indices with suitable properties are obtained. We derive tha asymptotic distribution of the family { $C_{p}$(.alpha.,.beta.); .alpha..geq.0,.beta..geq.0} under general proper conditions. It is also shown that the bootstrap approximation to the distribution of the estimator $C_{p}$(.alpha., .beta.) is vaild for almost all sample sequences. These asymptotic distributions would be used in constructing some bootstrap confidence intervals.tervals.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.363-375
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• 2004

In this paper, We show that the bandpass random signals of the form ∑$_{\alpha}$$\alpha$$_{\alpha}$ a Sin(2$\pi$f$_{\alpha}$t + b$_{\alpha}$) where a$_{\alpha}$ being a random number in [0,1], f$_{\alpha}$ a random integer in a given frequency band, and b$_{\alpha}$ a random number in [0, 2$\pi$], generate Gaussian white noise signals and hence they are adequate for simulating Continuous Markov processes. We apply the result to the fluctuation-dissipation formula for the Johnson noise and show that the probability distribution for the long term average of the power of the Johnson noise is a X$^2$ distribution and that the relative error of the long term average is (equation omitted) where N is the number of blocks used in the average.error of the long term average is (equation omitted) where N is the number of blocks used in the average.

• International Journal of Advanced Culture Technology
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• v.5 no.3
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• pp.67-72
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• 2017

Transform variation technique is constituted the vibration status of the flash-gap recognition level (FGRL) on the distribution recognition function. The recognition level condition by the distribution recognition function system is associated with the scattering vibration system. As to search a position of the dot model, we are consisted of the distribution value with character point by the output signal. The concept of recognition level is composed the reference of flash-gap level for variation signal by the distribution vibration function. For displaying a variation of the FGRL of the maximum-average in terms of the vibration function, and distribution position vibration that was the a distribution value of the far variation of the $Dis-rf-FA-{\alpha}_{MAX-AVG}$ with $5.74{\pm}1.12$ units, that was the a distribution value of the convenient variation of the $Dis-rf-CO-{\alpha}_{MAX-AVG}$ with $1.64{\pm}0.16$ units, that was the a distribution value of the flank variation of the $Dis-rf-FL-{\alpha}_{MAX-AVG}$ with $0.74{\pm}0.24$ units, that was the a distribution value of the vicinage variation of the $Dis-rf-VI-{\alpha}_{MAX-AVG}$ with $0.12{\pm}0.01$ units. The scattering vibration will be to evaluate at the ability of the vibration function with character point by the distribution recognition level on the FGRL that is showed the flash-gap function by the recognition level system. Scattering recognition system will be possible to control of a function by the special signal and to use a distribution data of scattering vibration level.

• East Asian mathematical journal
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• v.35 no.1
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• pp.67-75
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• 2019

We investigate the averaging value of a random sampling of a Dirichlet series with some condition using Poisson distribution. Our result is the following: Let $L(s)={\sum}^{\infty}_{n=1}{\frac{a_n}{n^s}}$ be a Dirichlet series that converges absolutely for Re(s) > 1. If $X_t$ is an increasing random sampling with Poisson distribution and there exists a number $0<{\alpha}<{\frac{1}{2}}$ such that ${\sum}_{n{\leq}u}a_n{\ll}u^{\alpha}$, then we have $${\mathbb{E}}L(1/2+iX_t)=O(t^{\alpha}{\sqrt{{\log}t}})$$, for all sufficiently large t in ${\mathbb{R}}$. As a result, we get the behaviour of $L({\frac{1}{2}}+it)$ such that L is a Dirichlet L-function or a modular L-function, when t is sampled by the Poisson distribution.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.541-550
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• 2007

This paper presents characterizations of the power distribution with the parameter $\beta=1$ by the independence of the lower record values. We prove $X\;{\in}\;POW({\alpha},\;1)$ for ${\alpha}\;>\;0$, if and only if $\frac{X_{L(n)}}{X_{L(m)}}$ and $X_{L(m)}$ for $1\;{\leq}\;m\;<\;n$ are independent. And we prove that $X\;{\in}\;POW({\alpha},\;1)$ for ${\alpha}\;>\;0$, if and only if $\frac{X_{L(m)}-X_{L(m+1)}}{X_{L(m)}}$ and $X_{L(m)$ for $m\;{\geq}\;1$ are independent or $\frac{X_{L(m)}-X_{L(m+1)}}{X_{L(m+1)}}$ and $X_{L(m)}$ for $m\;{\geq}\;1$ are independent.