• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.141-149
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• 1995

Let N denote the set of positive integers. Fix $d_1, d_2 \in N with d = d_1 + d_2$. Let X and Y be real random variables and let ${X_i : i \in N^d_1} and {Y_j : j \in N^d_2}$ be independent families of independent identically distributed random variables with $L(X) = L(X_i) and L(Y) = L(Y_j)$, where $L(\cdot)$ denote the law of $\cdot$.

• Journal of Ocean Engineering and Technology
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• v.33 no.3
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• pp.222-228
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• 2019

An extreme value analysis (EVA) is essential to obtain a design value for highly nonlinear variables such as long-term environmental data for wind and waves, and slamming or sloshing impact pressures. According to the extreme value theory (EVT), the extreme value distribution is derived by multiplying the initial cumulative distribution functions for independent and identically distributed (IID) random variables. However, in the position mooring of DNVGL, the sampled global maxima of the mooring line tension are assumed to be IID stochastic variables without checking their independence. The ITTC Recommended Procedures and Guidelines for Sloshing Model Tests never deal with the independence of the sampling data. Hence, a design value estimated without the IID check would be under- or over-estimated because of considering observations far away from a Weibull or generalized Pareto distribution (GPD) as outliers. In this study, the IID sampling data are first checked in an EVA. With no IID random variables, an automatic resampling scheme is recommended using the block maxima approach for a generalized extreme value (GEV) distribution and peaks-over-threshold (POT) approach for a GPD. A partial autocorrelation function (PACF) is used to check the IID variables. In this study, only one 5 h sample of sloshing test results was used for a feasibility study of the resampling IID variables approach. Based on this study, the resampling IID variables may reduce the number of outliers, and the statistically more appropriate design value could be achieved with independent samples.

• Journal of Communications and Networks
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• v.1 no.2
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• pp.111-117
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• 1999

Using a method recently reported in the literature for analyzing the bit error probability (BEP) performance of noncoherent Mary orthogonal signals with square-law combining in the presence of independent and identically distributed Nakagami-m faded paths, we are able to reformulate this method so as to apply to a generalized fading channel in which the fading in each path need not be identically distributed nor even distributed ac-cording to the same family of distribution. The method leads to exact expressions for the BEP in the form of a finite-range integral whose integrand involves the moment generating function of the combined signal-to-noise ratio and which can therefore be readily evaluated numerically. The mathematical formalism is illustrated by applying the method to some selected numerical examples of interest showing the impact of the multipath intensity profile (MIP) as well as the fading correlation profile (FCP) on the BEP performance of M-ary orthogonal signal over Nakagami-m fading channels. Thses numerical results show that both MIP and FCP induce a non-negligible degradition in the BEP and have therefore to be taken into account for the accurate prediction of the performance of such systems.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.85-89
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• 2011

We present characterizations of the Pareto distribution by the independent property of upper record values in such a way that F(x) has a Pareto distribution if and only if $\frac{X_{U(n)}}{X_{U(m)}}$ and $X_{U(m)}$ are independent for $1{\leq}m. Futhermore, the characterizations should find that F(x) has a Pareto distribution if and only if $\frac{X_{U(n)}}{X_{U(n)}{\pm}X_{U(m)}}$ and $X_{U(m)}$ are independent for $1{\leq}m.

• Journal of the Korean Statistical Society
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• v.34 no.1
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• pp.11-20
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• 2005

The distributional properties of R = X/(X + Y) and related estimation procedures are derived when X and Y are independent and identically distributed according to the Weibull or Levy distribution. The work is of interest in biological and physical sciences, econometrics, engineering and ranking and selection.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.65-66
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• 2007

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.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.647-653
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• 2012

In this paper, we consider fuzzy random sets as (measurable) mappings from a probability space into the set of fuzzy sets and prove a uniform strong law of large numbers for sequences of independent and identically distributed fuzzy random sets. Our results generalize those of Bass and Pyke(1984)and Jang and Kwon(1998).

• 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].

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.21-24
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• 2003

In the recent papers by Harris and Park (1994) and by Hui and Park (2000), a family of lattice distributions derived from a sum of independent identically distributed random variables is examined. In this paper we generalize a result of Hui and Park (2000) on lattice distributions on the torus using the Poisson summation formula.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.15 no.25
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• pp.75-82
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• 1992

Standard acceptance sampling plans models the production pricess as a sequence of independent identically distributed Beruoulli random variables. However, the quality of items sampled sequentially from an ongoing production process of ten exhibits statistical dependency that is not accounted for in standard acceptance sampling plans. In this paper, a dependent production process is modelled as an ARMA process and as a two-state Markov chain. A simulation study of each is performed. A comparison of the probability of acceptance is done for the simulation method and for the approximation method.