• The Pure and Applied Mathematics
• /
• v.4 no.1
• /
• pp.97-104
• /
• 1997

The large deviations theorem of Cramer is extended to conditional probabilities in the following sense. Consider a random sample of pairs of random vectors and the sample means of each of the pairs. The probability that the first falls outside a certain convex set given that the second is fixed is shown to decrease with the sample size at an exponential rate which depends on the Kullback-Leibler distance between two distributions in an associated exponential familiy of distributions. Examples are given which include a method of computing the Bahadur exact slope for tests of certain composite hypotheses in exponential families.

• International Journal of Reliability and Applications
• /
• v.18 no.2
• /
• pp.65-82
• /
• 2017

Abstract. Camilo Dagum proposed several variants of a new model for the size distribution of personal income in a series of papers in the 1970s. He traced the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. The main aim of this paper is to define a bivariate Dagum distribution so that the marginals have Dagum distributions. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in closed forms. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance-covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.

• Journal of the Korean Statistical Society
• /
• v.19 no.1
• /
• pp.24-44
• /
• 1990

The purpose of this paper is to extend the idea of Tamhane and Bechhofer (1977, 1979) concerning the normal means problem to some general class of distributions. The key idea in Tamhane and Bechhofer is the derivation of the computable lower bounds on the probability of a correct selection. To derive such lower bounds, they used the specific covariance structure of a multivariate normal distribution. It is shown that such lower bounds can be obtained for a class of stochastically increasing distributions under certain conditions, which is sufficiently general so as to include the normal means problem as a special application. As an application of the general theory to the scale parameters problem, a two-stage elimination type procedure for selecting the population associated with the smallest variance from among several normal populations is proposed. The design constants are tabulated and the relative efficiencies are computed.

• Journal of the military operations research society of Korea
• /
• v.11 no.1
• /
• pp.1-7
• /
• 1985

A computer-aided simulation model for inventory control was developed using Apple II Plus micro-computer. The model forecasts quarterly demands with Single Exponential Smoothing method and simulates Supply Demand Review and Inventory Level Settings for each items. The simulation is based on the assumption that the demand occurrences have their own probability distributions.

• Korean Journal of Mathematics
• /
• v.8 no.2
• /
• pp.111-119
• /
• 2000

For a linear operator Q from $R^d$ into $R^d$. ${\alpha}$ > 0 and 0 < $b$ < 1, the Gaussian (Q, $b$, ${\alpha}$)-semi-stability of probability measures on $R^d$ is investigated.

• 전기의세계
• /
• v.29 no.11
• /
• pp.742-750
• /
• 1980

The problem of nonlinear time-invariant system identification by estimation of Wiener kernels is studied for discrete time systems with inputs having symmetric probability distributions. G-functionals are constructed. It is further shown that under idealized conditions, these seemingly different techniques yield the same results. The results of identification of asimulated second degree system is presented.

• Journal of the Korean Statistical Society
• /
• v.7 no.1
• /
• pp.11-16
• /
• 1978

Bayesian procedures are in vogue to revise the parameter estimates of the forecasting model in the light of actual time series data. In this paper, we study the Bayes forecast for demand and the risk when (a) 'noise' and (b) mean demand rate in a constant process model have moderately non-normal probability distributions.

• Communications for Statistical Applications and Methods
• /
• v.6 no.3
• /
• pp.677-686
• /
• 1999

In this paper we introduce a class of moving-average(MA) sequences of multivariate random vectors with geometric marginals. The theory of positive dependence is used to show that in various cases the class of MA sequences consists of associated random variables. We utilize positive dependence properties to obtain weakly probability inequality of the multivariate processes.

• Journal of The Korean Society of Agricultural Engineers
• /
• v.60 no.3
• /
• pp.63-70
• /
• 2018

In this study, a simple probabilistic approach using equivalent coefficient of consolidation ($c_e$) was proposed to consider the spatial variability of coefficient of vertical consolidation ($c_v$), and the effect of the probability distribution of coefficient of consolidation on degree of consolidation in heterogeneous soil was investigated. The statistical characteristics of consolidation coefficient were estimated from 1,226 field data, and four probability distributions (Normal, Log-normal, Gamma, and Weibull) were applied to consider the effect of probability distribution. The random fields of coefficient of consolidation were generated based on Karhunen-Loeve expansion. Then, the equivalent coefficient of consolidation was calculated from the random field and used as the input value of consolidation analysis. As a result, the probabilistic analysis can be performed effectively by separating random field and numerical analysis, and probabilistic analysis was performed using a Latin hypercube Monte Carlo simulation. The results showed that the statistical properties of $c_e$ were changed by the probability distribution and spatial variability of $c_v$, and the probability distribution of $c_v$ has considerable effects on the probabilistic results. There was a large difference of failure probability depend on the probability distribution when the autocorrelation distance was small (i.e., highly heterogeneous soil). Therefore, the selection of a suitable probability distribution of $c_v$ is very important for reliable probabilistic analysis of consolidation.

• The Korean Journal of Applied Statistics
• /
• v.22 no.2
• /
• pp.237-248
• /
• 2009

The probability of default on the credit evaluation study is represented as a linear combination of two distributions of default and non-default, and the distribution of the probability of default are generally known in most cases. Except the well-known Kolmogorov-Smirnov statistic for testing the identity of two distribution, Kuiper, Cramer-Von Mises, Anderson-Darling, and Watson test statistics are introduced in this work. Under the assumption that the population distribution is known, modified Cramer-Von Mises, Anderson-Darling, and Watson statistics are proposed. Based on score data generated from various probability density functions of the probability of default, the modified test statistics are discussed and compared.