• Journal of the korean society of oceanography
• /
• 제33권3호
• /
• pp.113-122
• /
• 1998

The requisite numbers of sample replicates for the population study of soft-bottom benthos were estimated from survey data on the Songdo tidal flat and subtidal zone in Youngil Bay, Korea. Large numbers of samples were taken; two-hundred-fifty 0.02 m$^2$ box corers and fifty 0.1m$^2$ van Veen grabs were taken on the Songdo tidal flat and in Youngil Bay, respectively. The effect of sampler size on sampling efforts was investigated by pooling the unit samples in pairs, fours, eights, etc. The requisite number of sample replicates (n$_r$) was determined by sample variance (s$^2$) and mean (m) function (n$_r$:s$^2$/P$^2$m$^2$), at P=0.2 level, in which s$^2$ and m were calculated from the counts of individuals collected. For example, seven samples of 0.02 m$^2$ corer for the intertidal and two samples of 0.1 m$^2$ van Veen grab for subtidal fauna were required to estimate the total density of community. The smaller sampler size was more efficient than larger ones when sampling costs were compared on the basis of the total sampling area. The requisite number of sample replicates was also predicted ($\^{n}$n$_r$) by substituting $\^{s}$$^2$ obtained from the regression of s$^2$ against m using the Taylor's power law ($\^{s}$$^2$:am$^b$). The regression line of survey data on s$^2$ and m plotted on log scale was well fitted to the Taylor's power law (r$^2$${\geq}$0.95, p<;0.001) over the whole range of m. The exponent b was, however, varied when it was estimated from m which was categorized into classes by its scale. The fitted exponent b was large when both density class and the sampler size were large. The number of sample replicates, therefore, could be more significantly estimated, if regression coefficients (a and b) would be calculated from sample variance and mean categorized into density classes.

• 전자공학회논문지B
• /
• 제33B권7호
• /
• pp.107-115
• /
• 1996

The average distortio of the vector quantizer is calcualted using a probability function F of the input source for a given codebook. But, since the input source is unknown in geneal, using the sample vectors that is realized from a random vector having probability function F, a time-average opeation is employed so as to obtain an approximation of the average distortion. In this case the size of the smple set should be large so that the sample vectors represent true F reliably. The theoretical inspection about the approximation, however, is not perfomed rigorously. Thus one might use the time-average distortion without any verification of the approximation. In this paper, the convergence characteristics of the time-average distortions are theoretically investigated when the size of sample vectors or the size of codebook gets large. It has been revealed that if codebook size is large enough, then small sample set is enough to obtain the average distortion by approximatio of the calculated tiem-averaged distortion. Experimental results on synthetic data, which are supporting the analysis, are also provided and discussed.

• 한국신뢰성학회지:신뢰성응용연구
• /
• 제12권4호
• /
• pp.265-274
• /
• 2012

We in this paper discuss the strong law of large numbers for weighted sums of arrays of rowwise LNQD random variables by using a new exponential inequality of LNQD r.v.'s under suitable conditions and we obtain one of corollary.

• Journal of applied mathematics & informatics
• /
• 제39권1_2호
• /
• pp.145-153
• /
• 2021

When {Xni|1 ≤ i ≤ n, n ≥ 1} be an array of rowwise negatively superadditive dependent(NSD) for semi-Gaussian random variables and {ani|1 ≤ i ≤ n, n ≥ 1} is an array of constants, we study the almost sure convergence of weighted sums ∑ni=1 aniXni under some appropriate conditions and we obtain some corollaries.

• 대한수학회논문집
• /
• 제18권2호
• /
• pp.375-383
• /
• 2003

Under some conditions on an array of rowwise independent random variables, Hu et at. (1998) obtained a complete convergence result for law of large numbers with rate {a$\_$n/, n $\geq$ 1} which is bounded away from zero. We investigate the general situation for rate {a$\_$n/, n $\geq$ 1) under similar conditions.

• International Journal of Reliability and Applications
• /
• 제1권2호
• /
• pp.123-131
• /
• 2000

This paper concerns with the consistent estimator for the fuzzy expectation of a random variable taking values in the space F($R^p$) of upper semicontinuous convex fuzzy subsets of $R^p$ with compact support. We introduce the concept of a fuzzy sample mean and show that the fuzzy sample mean is a strong consistent estimator for the fuzzy expectation. Some examples are given to illustrate the main result.

• Journal of applied mathematics & informatics
• /
• 제27권3_4호
• /
• pp.885-893
• /
• 2009

In this paper we study the strong law of large numbers for weighted average of pairwise negatively quadrant dependent random variables. This result extends that of Jamison et al.(Convergence of weight averages of independent random variables Z. Wahrsch. Verw Gebiete(1965) 4 40-44) to the negative quadrant dependence.

• 대한수학회지
• /
• 제54권3호
• /
• pp.877-896
• /
• 2017

In this paper, the complete convergence and complete moment convergence for a class of random variables satisfying the Rosenthal type inequality are investigated. The sufficient and necessary conditions for the complete convergence and complete moment convergence are provided. As applications, the Baum-Katz type result and the Marcinkiewicz-Zygmund type strong law of large numbers for a class of random variables satisfying the Rosenthal type inequality are established. The results obtained in the paper extend the corresponding ones for some dependent random variables.

• Communications for Statistical Applications and Methods
• /
• 제12권2호
• /
• pp.275-283
• /
• 2005

In this paper, we give a sufficient condition for convergence in probability of weighted sums of convex-compactly uniformly integrable fuzzy random variables. As a result, we obtain weak law of large numbers for weighted sums of convexly tight fuzzy random variables.

• 대한수학회지
• /
• 제53권6호
• /
• pp.1275-1292
• /
• 2016

The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to (0, ${\infty}$) instead of (0, 2), we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.