• Korean Journal of Mathematics
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• v.21 no.4
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• pp.429-437
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• 2013

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be independent and identically distributed random variables having common exponential density with unknown mean ${\mu}$. In the sequential confidence interval estimation for the exponential hazard rate ${\theta}=1/{\mu}$, when the loss function is strictly convex, the following stopping rule is proposed with the half length d of prescribed confidence interval $I_n$ for the parameter ${\theta}$; ${\tau}$ = smallest integer n such that $n{\geq}z^2_{{\alpha}/2}\hat{\theta}^2/d^2+2$, where $\hat{\theta}=(n-1)\bar{X}{_n}^{-1}/n$ is the minimum risk estimator for ${\theta}$ and $z_{{\alpha}/2}$ is defined by $P({\mid}Z{\mid}{\leq}{\alpha}/2)=1-{\alpha}({\alpha}{\in}(0,1))$ Z ~ N(0, 1). For the confidence intervals $I_n$ which is required to satisfy $P({\theta}{\in}I_n){\geq}1-{\alpha}$. These estimated intervals $I_{\tau}$ have the asymptotic consistency of the sequential procedure; $$\lim_{d{\rightarrow}0}P({\theta}{\in}I_{\tau})=1-{\alpha}$$, where ${\alpha}{\in}(0,1)$ is given.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.127-131
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• 2003

Let X$_1$, X$_2$,... be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X$_j$ is an upper record value of this sequence if X$_j$ > max {X$_1$,X$_2$,...,X$_{j-1}$}. We define u(n)=min{j$\mid$j> u(n-1), X$_j$ > X$_{u(n-1)}$, n $\geq$ 2} with u(1)=1. Then F(x) = 1-x$^{\theta}$, x > 1, ${\theta}$ < -1 if and only if (${\theta}$+1)E[X$_{u(n+1)}$$\mid$X$_{u(m)}$=y] = ${\theta}E[X_{u(n)}$\mid$X_{u(m)}=y], (\theta+1)^2E[X_{u(n+2)}$\mid$X_{u(m)}=y] = \theta^2E[X_{u(n)}$\mid$X_{u(m)}=y], or (\theta+1)^3E[X_{u(n+3)}$\mid$X_{u(m)}=y] = \theta^3E[X_{u(n)}$\mid$X_{u(m)}=y], n $\geq$ M+1$.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.535-540
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• 2002

Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.497-503
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• 2005

This paper presents characterizations on the independence of the exponential and Pareto distributions by record values. Let ${X_{n},\;n {\ge1}$ be a sequence of independent and identically distributed(i.i.d) random variables with a continuous cumulative distribution function(cdf) F(x) and probability density function(pdf) f(x). $Let{\;}Y_{n} = max{X_1, X_2, \ldots, X_n}$ for n \ge 1. We say $X_{j}$ is an upper record value of ${X_{n},{\;}n\ge 1}, if Y_{j} > Y_{j-1}, j > 1$. The indices at which the upper record values occur are given by the record times {u(n)}, n \ge 1, where u(n) = $min{j|j > u(n-1), X_{j} > X_{u(n-1)}, n \ge 2}$ and u(l) = 1. Then F(x) = $1 - e^{-\frac{x}{a}}$, x > 0, ${\sigma} > 0$ if and only if $\frac {X_u(_n)}{X_u(_{n+1})} and X_u(_{n+1}), n \ge 1$, are independent. Also F(x) = $1 - x^{-\theta}, x > 1, {\theta} > 0$ if and only if $\frac {X_u(_{n+1})}{X_u(_n)}{\;}and{\;} X_{u(n)},{\;} n {\ge} 1$, are independent.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.12
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• pp.3118-3134
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• 2013

This paper deliberates for a multimedia transmission scheme combining multiple description coding (MDC) and network coding (NC). Our goal is to take advantage from the property of MDC to provide quantized and compressed independent and identically distributed (iid) descriptions and also from the benefit of network coding, which uses network resources efficiently to recover lost data in the network. Recently, p-cycle NC has been introduced to recover and protect any lost or distorted descriptions at the receiver part exactly without need of retransmission. So far, MDC have not been explored using this type of NC. Compressed and coded descriptions are transmitted through the network where p-cycle NC is applied. P-cycle based algorithm is proposed for single and multiple descriptions lost. Results show that in the fixed bit rate, the PSNR (Peak Signal to Noise Ratio) of our reconstructed image and also subjective evaluation is improved significantly compared to previous work which is averaging method joint with MDC in order to conceal lost descriptions.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.1
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• pp.102-122
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• 2017

Nanotechnology has provided a set of tools that the engineers can use to design and manufacture integrated nano devices, which are capable of performing sensing, computing, data storing and actuation. One of the main hurdles for nano devices has been the amount of power that it can generate for transmission of data. In this paper, we proposed cooperative nano communication in the Terahertz (THz) Gap frequency band to increase the range of transmission. Outage probability (OP) performances for the proposed cooperative nano communication networks in the THz band (0.1 - 10THz) have been evaluated for the following scenarios; A) A single decode-and-forward (DF) relay over independent identically distributed (i.i.d.) Rayleigh fading channels, B) DF multi-relay network with best relay selection (BRS) over i.i.d. Rayleigh fading channels, and C) DF multi-relay network with multiple hops with BRS over i.i.d. Rayleigh fading channels. The results show that the transmission distance can be improved significantly by employing DF relays. Also, it is shown that by increasing the number of hops in a relay the OP performance is marginally degraded. The analytical results have been verified by Monte-Carlo simulation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.10
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• pp.5035-5057
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• 2019

Advancements in nanotechnology and novel nano materials in the past decade have provided a set of tools that can be used to design and manufacture integrated nano devices, which are capable of performing sensing, computing, data storing and actuation. In this paper, we have proposed cooperative nano communication using Power Switching Relay (PSR) Wireless Power Transfer (WPT) protocol and Time Switching Relay (TSR) WPT protocol over independent identically distributed (i.i.d.) Rayleigh fading channels in the Terahertz (THz) Gap frequency band to increase the range of transmission. Outage Probability (OP) performances for the proposed cooperative nano communication networks have been evaluated for the following scenarios: A) A single decode-and-forward (DF) relay for PSR protocol and TSR protocol, B) DF multi-relay network with best relay selection (BRS) for PSR protocol and TSR protocol, and C) DF multi-relay network with multiple DF hops with BRS for PSR protocol and TSR protocol. The results have shown that the transmission distance can be improved significantly by employing DF relays with WPT. They have also shown that by increasing the number of hops in a relay the OP performance is only marginally degraded. The analytical results have been verified by Monte-Carlo simulations.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.12A
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• pp.1244-1250
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• 2007

User cooperation provides high reliability in wireless communication systems by employing relay nodes to transmit the same information. In this paper, a bit error rate (BER) study is presented for decode-and-forward (DF) relaying for user cooperation in independent and identically distributed Rayleigh fading channels. For an arbitrary number of relays, exact and closed-form expressions of the BER are proposed for M-ary PAM (Pulse Amplitude Modulation), QAM (Quadrature Amplitude Modulation) and PSK (Phase Shift Keying), respectively. It is also shown that the analytic results are perfectly matched with the simulated ones.

• Journal of the Korean Data and Information Science Society
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• v.27 no.4
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• pp.1067-1074
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• 2016

A start-up demonstration test is a mechanism that is usually used to determine the reliability of equipment, for example water pumps, car batteries and power generators. The simplest and oldest start-up demonstration tests are called CS (consecutive successes) which have been studied by Hahn and Gage (1983), Viveros and Balakrishnan (1993).At first Hahn and Gage (1983) discussed the start-up demonstration test. I was based on i.i.d (independently and identically distributed) binary outcomes with the specified number of consecutive successful start-ups. Oh (2016) studied CSNCF (consecutive successful, but not consecutive failures). In this paper, we investigated the CS and CSNCF models, also their applications to start-up demonstration tests. The numerical results showed that the expectations and variances of the total number of attempted start-ups until the acceptance of the unit are gradually increasing in all of the specified number of successes as the p (probability of a successful start-up in an single trial) decreases from 0.99 to 0.90. The difference between means of the CS mode and CSNCF model is small, but variances of the CS and CSNCF are big.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.6C
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• pp.523-531
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• 2005

We derive decision regions of the maximum likelihood(ML) and suboptimum ML(S-ML) detectors in the first order moving average(FOMA) of an impulsive process. The ML and S-ML detectors are compared in terms of the bit-error-rate in the antipodal signaling system. Numerical results show that the S-ML detector, despite its reduced complexity and simpler structure, exhibits practically the same performance as the optimum ML detector. It is also shown that the performance gap between detectors for FOMA and independent and identically distributed noise becomes larger as the degree of noise impulsiveness increases.