• Title/Summary/Keyword: Distribution Department

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Asymptotically Distribution-Free Procedure in a Two-Way Layout

  • Park, Young-Hun
    • Journal of the Korean Statistical Society
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    • v.24 no.2
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    • pp.375-387
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    • 1995
  • Main purpose of this article is to consider the asymptotic distribution of the rank transformed F statistic for interaction in a two-way layout. Some theorems and sufficient conditions are derived to have the rank transformed F statistic converged in distribution to a chi-squared random variable with (I-1)(J-1) degrees of freedom divided by (I-1)(J-1). These results will be useful for the other theoretical studies of the rank transform procedure in experimental designs.

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SIZE DISTRIBUTION OF ONE CONNECTED COMPONENT OF ELLIPTIC RANDOM FIELD

  • Alodat, M.T.
    • Journal of the Korean Statistical Society
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    • v.36 no.4
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    • pp.479-488
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    • 2007
  • The elliptic random field is an extension to the Gaussian random field. We proved a theorem which characterizes the elliptic random field. We proposed a heuristic approach to derive an approximation to the distribution of the size of one connected component of its excursion set above a high threshold. We used this approximation to approximate the distribution of the largest cluster size. We used simulation to compare the approximation with the exact distribution.

Estimation for scale parameter of type-I extreme value distribution

  • Choi, Byungjin
    • Journal of the Korean Data and Information Science Society
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    • v.26 no.2
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    • pp.535-545
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    • 2015
  • In a various range of applications including hydrology, the type-I extreme value distribution has been extensively used as a probabilistic model for analyzing extreme events. In this paper, we introduce methods for estimating the scale parameter of the type-I extreme value distribution. A simulation study is performed to compare the estimators in terms of mean-squared error and bias, and the obtained results are provided.

ROC Curve for Multivariate Random Variables

  • Hong, Chong Sun
    • Communications for Statistical Applications and Methods
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    • v.20 no.3
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    • pp.169-174
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    • 2013
  • The ROC curve is drawn with two conditional cumulative distribution functions (or survival functions) of the univariate random variable. In this work, we consider joint cumulative distribution functions of k random variables, and suggest a ROC curve for multivariate random variables. With regard to the values on the line, which passes through two mean vectors of dichotomous states, a joint cumulative distribution function can be regarded as a function of the univariate variable. After this function is modified to satisfy the properties of the cumulative distribution function, a ROC curve might be derived; moreover, some illustrative examples are demonstrated.

On Asymptotic Properties of a Maximum Likelihood Estimator of Stochastically Ordered Distribution Function

  • Oh, Myongsik
    • Communications for Statistical Applications and Methods
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    • v.20 no.3
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    • pp.185-191
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    • 2013
  • Kiefer (1961) studied asymptotic behavior of empirical distribution using the law of the iterated logarithm. Robertson and Wright (1974a) discussed whether this type of result would hold for a maximum likelihood estimator of a stochastically ordered distribution function; however, we show that this cannot be achieved. We provide only a partial answer to this problem. The result is applicable to both estimation and testing problems under the restriction of stochastic ordering.

An Investigation into the Impact on Voltage Sag due to Faults in Low Voltage Power Distribution Systems

  • Aggarwal R. K.
    • KIEE International Transactions on Power Engineering
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    • v.5A no.2
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    • pp.97-102
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    • 2005
  • Voltage sags are the most widespread quality issues affecting distribution systems. This paper describes in some detail the voltage sag characteristics due to different types and locations of fault in a practical low voltage power distribution system encountered in the UK. The results not only give utility engineers very useful information when identifying parts of the system most likely to pose problems for customer equipments, but also assist the facility personnel to make decisions on purchasing power quality mitigation equipment.

A Note on the Simple Chi-Squared Test of Multivariate Normality

  • Park, Cheol-Yong
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.2
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    • pp.423-430
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    • 2004
  • We provide the exact form of a Rao-Robson version of the chi-squared test of multivariate normality suggested by Park(2001). This test is easy to apply in practice since it is easily computed and has a limiting chi-squared distribution under multivariate normality. A self-contained formal argument is provided that it has the limiting chi-squared distribution. A simulation study is provided to study the accuracy, in finite samples, of the limiting distribution. Finally, a simulation study in a nonnormal distribution is conducted in order to compare the power of our test with those of other popular normality tests.

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On Characterizing Distributions by Some Properties of the Distribution Truncated at the rth order Statistic

  • Sangun Park
    • Communications for Statistical Applications and Methods
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    • v.1 no.1
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    • pp.52-56
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    • 1994
  • When we have an i.i.d. sample of size n from a continuous distribution, the distribution truncated on the left at the rth order statistic plays an important role in the theoretical analysis of the Type 2 censored data. The charaterization of distributions by the average of the conditional expectation and the average of the conditional information concerning the truncated distribution is studied here.

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Estimation in a Half-Triangle Distribution Based on Multiply Type-II Censored Samples

  • Kang, Suk-Bok
    • Journal of the Korean Data and Information Science Society
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    • v.18 no.3
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    • pp.793-801
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    • 2007
  • For multiply Type-II censored samples from a half-triangle distribution, the maximum likelihood method does not admit explicit solutions. In this case, we propose some explicit estimators of the location parameter in the half-triangle distribution by the approximate maximum likelihood methods. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

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Likelihood ratio in estimating Chi-square parameter

  • Rahman, Mezbahur
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.3
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    • pp.587-592
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    • 2009
  • The most frequent use of the chi-square distribution is in the area of goodness-of-t of a distribution. The likelihood ratio test is a commonly used test statistic as the maximum likelihood estimate in statistical inferences. The recently revised versions of the likelihood ratio test statistics are used in estimating the parameter in the chi-square distribution. The estimates are compared with the commonly used method of moments and the maximum likelihood estimate.

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