• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.12
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• pp.6161-6176
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• 2018

Pseudorandom numbers are useful in cryptographic operations for using as nonce, initial vector, secret key, etc. Security of the cryptosystem relies on the secret key parameters, so a good pseudorandom number is needed. In this paper, we have proposed a new approach for generation of pseudorandom number. This method uses the three dimensional combinational puzzle Rubik Cube for generation of random numbers. The number of possible combinations of the cube approximates to 43 quintillion. The large possible combination of the cube increases the complexity of brute force attack on the generator. The generator uses cryptographic hash function. Chaotic map is being employed for increasing random behavior. The pseudorandom sequence generated can be used for cryptographic applications. The generated sequences are tested for randomness using NIST Statistical Test Suite and other testing methods. The result of the tests and analysis proves that the generated sequences are random.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.507-519
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• 2012

In this paper we obtain the complete moment convergence for an array of rowwise extended negative orthant dependent random variables. By using the result we can prove the complete moment convergence for some positively orthant dependent sequence satisfying the extended negative orthant dependence.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.419-425
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• 1996

Let ${X, X_n, n \geq 1}$ be a sequence of independent and identically distributed(i.i.d) random variables with EX = 0 and $E$\mid$X$\mid$^p < \infty$ for some $p \geq 1$. Let ${a_{ni}, 1 \leq i \leq n, n \geq 1}$ be a triangular arrary of constants. The almost sure(a.s) convergence of weighted sums $\sum_{i=1}^{n} a_{ni}X_i$ can be founded in Choi and Sung[1], Chow[2], Chow and Lai[3], Li et al. [4], Stout[6], Sung[8], Teicher[9], and Thrum[10].

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.247-257
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• 2007

Consider the heteroscedastic regression model $Y_i=g(x_i)+{\sigma}_i\;{\epsilon}_i=(1{\leq}i{\leq}n)$, where ${\sigma}^2_i=f(u_i)$, the design points $(x_i,\;u_i)$ are known and nonrandom, and g and f are unknown functions defined on closed interval [0, 1]. Under the random errors $\epsilon_i$ form a sequence of NA random variables, we study the asymptotic normality of wavelet estimators of g when f is a known or unknown function.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.327-335
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• 2004

In this paper, we reformulate a snapshot attractor([5]), ($K,\;\={\mu_{\iota}}$) generated by a random baker's map with a sequence of probability measures {\={\mu_{\iota}}} on K. We obtain bounds of the correlation dimensions of ($K,\;\={\mu_{\iota}}$) for all ${\iota}\;{\geq}\;1$.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.291-296
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• 2000

Petrov(1996) examined the connection between general moment conditions and the applicability of the strong law lf large numbers to a sequence of pairwise independnt and identically distributed random variables. In this note wee generalize Theorem 1 of Petrov(1996) and also show that still holds under assumption of pairwise negative quadrant dependence(NQD).

• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.245-257
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• 2006

A modified Anderson and Hauck(1983) test for analyzing a two-sequence two-period crossover design in bioequivalence trials is proposed when some observations at the second period are missing. It is based on the maximum likelihood estimators of average bioequivalence model and designed for handling missing at random(MAR) situation. The performance of the proposed test is compared to other tests using Monte Carlo simulations.

• Proceedings of the KIEE Conference
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• 2005.04a
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• pp.157-160
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• 2005

본 연구에서는 고정 주파수의 캐리어 합성만으로 랜덤 주파수의 캐리어를 간단하게 발생하는 방법을 제안하였다. 고정 주파수를 갖는 삼각파 캐리어와 그 역상의 삼각파 캐리어를 랜덤 비트 발생기(PRBS : Pseudo Random Binary Sequence)에 의하여 선택하여 랜덤 주파수 캐리어를 새롭게 합성 할 수 있다. 실험과 시뮬레이션에 의하여 PRBS의 시트프 레지스터의 비트별 고조파 스펙트럼을 비교 고찰하였다.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.369-378
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• 2002

Strong laws of large numbers for weighted sums of asymptotically almost negatively associated(AANA) sequence are proved by our generalized maximal inequality for AANA random variables at a crucial step.

• Journal of the Korean Statistical Society
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• v.13 no.2
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• pp.87-106
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• 1984

It ${X_t}$ is a sequence of independent identically distributed normal random variables, then the conditional probability density of $X_1, X_2, \cdots, X_n$ given the first p+1 sample autocovariances converges to the maximum entropy probability density satisfying the corresponding covariance constraints as the length of the sample sequence tends to infinity. This establishes that the maximum entropy probability density and the associated Gaussian autoregressive process arise naturally as the answers of conditional limit problems.