• Communications for Statistical Applications and Methods
• /
• v.4 no.1
• /
• pp.255-258
• /
• 1997

We prove a conjecture of Yu. V. Prokhorov in general Banach Spaces ; let ($X_n$, n$\geq$1} be a sequence of independent identically and symmetrically distributed Banach valued random variables, then the relation $\mid$$\mid$$S_n$$\mid$$\mid$/$b_n$ -> 1 a.s. cannot hold for any choice of constants $b_n$.

• Communications for Statistical Applications and Methods
• /
• v.16 no.3
• /
• pp.541-547
• /
• 2009

We consider distribution, reliability and moment of ratio in two independent beta random variables X and Y, and reliability and $K^{th}$ moment of ratio are represented by a mathematical generalized hypergeometric function. We introduce an approximate maximum likelihood estimate(AML) of reliability and right-tail probability in the beta distribution.

• 전기의세계
• /
• v.28 no.3
• /
• pp.57-64
• /
• 1979

The static state estimation are divided into two groups; estimation and detection & identification. This paper centers on detection and identification algorithm. Especially, the identification of line errors is focused on and is performed by the extended W.L.S. algorithm with line swithching states. Here, line switching states mean the discrete values of line admittance which are influenced by unexpected line switching. The numerical results are obtained from the assumption that the noise vector is independent zero mean Gaussian random variables.

• Journal of the Korean Data and Information Science Society
• /
• v.20 no.5
• /
• pp.955-960
• /
• 2009

As we shall dene an exponentiated complementary power function distribution, we shall consider moments, hazard rate, and inference for parameter in the distribution. And we shall consider an inference of the reliability and distributions for the quotient and the ratio in two independent exponentiated complementary power function random variables.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.2
• /
• pp.149-153
• /
• 2009

Let {$X_{n},\;n\;\geq\;1$} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f(x). Suppose $X_{U(m)},\;m = 1,\;2,\;{\cdots}$ be the upper record values of {$X_{n},\;n\;\geq\;1$}. It is shown that the linearity of the conditional expectation of $X_{U(n+2)}$ given $X_{U(n)}$ characterizes the lomax, exponential and pareto distributions.

• Proceedings of the Korean Reliability Society Conference
• /
• 2000.11a
• /
• pp.411-411
• /
• 2000

Consider the problem of estimating the reliability of a multicomponent stress-strength system which functions if at least r of the k identical components simultaneously function. All stresses and strengths are assumed to be independent random variables with two parameter Weibull distributions. First, we derive reference priors and probability matching priors which are noninformative priors. We next investigate sufficient conditions for propriety of posteriors under reference priors and probability matching priors. Finally, we provide, using these priors, some numerical results for Bayes estimates of the reliability by applying Gibbs sampling technique.

• Communications of the Korean Mathematical Society
• /
• v.10 no.2
• /
• pp.409-417
• /
• 1995

We consider the $R^k$-valued $(k \geq 1)$ process ${X_n}$ generated by $X_n + 1 = f(X_n)+e_{n+1}$, where $f(x) = (h(x),x^{(1)},x^{(1)},\cdots,x{(k-1)})'$. We assume that h is a real-valued measuable function on $R^k$ and that $e_n = (e'_n,0,\cdot,0)'$ where ${e'_n}$ are independent and identically distributed random variables. We obtained a practical criteria guaranteeing a given process to be geometrically ergodic. Sufficient condition for transience is also given.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.495-510
• /
• 2012

Let $X_1$, $X_2$,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.

• Journal of applied mathematics & informatics
• /
• v.3 no.1
• /
• pp.55-64
• /
• 1996

Let $X_1, ....$X_P be p($\geq$2) independent random variables, where each X1 has a gamma distribution with $k_i and ${\heta}_i$. The problem is to simultaneously estimate p gammar parameters ${\heta}_i$ under entropy loss where the parameters are believed priori. Hierarchical bayes(HB) and empirical bayes(EB) estimators are investigated. Next computer simulation is studied to compute the risk percentage improvement of the HB, EB and the estimator of Dey et al.(1987) compared to MVUE of ${\heta}$.

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