• Journal of Korean Institute of Industrial Engineers
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• v.39 no.2
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• pp.109-118
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• 2013

We propose a method for estimating coefficients of AR (autoregressive) model which named MLPAR (Maximum Likelihood of Pearson system for Auto-Regressive model). In the present method for estimating coefficients of AR model, there is an assumption that residual or error term of the model follows the normal distribution. In common cases, we can observe that the error of AR model does not follow the normal distribution. So the normal assumption will cause decreasing prediction accuracy of AR model. In the paper, we propose the MLPAR which does not assume the normal distribution of error term. The MLPAR estimates coefficients of auto-regressive model and distribution moments of residual by using pearson distribution system and maximum likelihood estimation. Comparing proposed method to auto-regressive model, results are shown to verify improved performance of the MLPAR in terms of prediction accuracy.

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.581-589
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• 2005

The purpose of this thesis is to develop and introduce Add-in program which we can systematically, visually and dynamically study discrete probability distribution of binomial distribution, poisson distribution and hypergeometric distribution, and continuous probability distribution of normal distribution, exponential distribution, and the definition and characteristics of t distribution, F distribution and ${\chi}^2$ distribution to be driven from normal distribution, and graphs, the computation process of probability by using VBA which is the device of Excel.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.539-559
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• 2014

We derive the exact distribution of summation for random samples from uniform distribution and then compare the exact distribution with the approximated normal distribution obtained by the central limit theorem. To check the similarity between two distributions, we consider five existing normality tests based on the difference between the target normal distribution and empirical distribution: Anderson-Darling test, Kolmogorov-Smirnov test, Cramer-von Mises test, Shapiro-Wilk test and Shaprio-Francia test. For the purpose of comparison, those normality tests are applied to the simulated data. It can sometimes be difficult to derive an exact distribution. Thus, we try two different transformations to find out which transform is easier to get the exact distribution in terms of calculation complexity. We compare two transformations and comment on the advantages and disadvantages for each transformation.

• Asian Pacific Journal of Cancer Prevention
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• v.17 no.9
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• pp.4405-4408
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• 2016

Background: To investigate the characteristics of allelic distribution of IGF2 and H19 gene polymorphisms in molar tissues compared to normal placentas. Materials and Methods: Forty-nine specimens of molar tissues as well as 100 control normal placental tissues, delivered on the same days, were collected. Polymerase chain reaction (PCR) with restriction fragment length polymorphism (RFLP) on 2% agarose gel electrophoresis was conducted to determine the allelic distribution. The ApaI polymorphism within exon 9 of IGF2 and the RsaI polymorphism within exon 5 of H19 were employed to identify the allelic distribution of the IGF2 and H19 genes, respectively. Then the data for these genes in the molar and normal placenta tissues were compared. Results: The allelic distribution of IGF2 genes found in molar tissue were 21 (42.9%) aa (undigested), 10 (20.4%) ab (heterozygous) and 18 (36.7%) bb (digested), while in normal placenta tissue the values were 22 (22%) aa, 51 (51%) ab, and 27 (27%) bb. The allelic distribution of H19 in molar tissues was 8 (16.2%) aa (undigested), 8 (16.3%) ab (heterozygous) and 33 (67.4%) bb (digested) and in normal placental tissue was 16 (16%) aa, 36 (36%) ab and 48 (48%) bb in normal placenta tissue. These results were significantly different with P values of 0.001 and 0.037 for the allelic distribution of IGF2 and H19, respectively. Conclusions: Molar tissues showed significant differences of allelic distribution of IGF2 and H19 from normal placenta tissues.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1211-1219
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• 2013

Recently, the usage of skew-normal distribution, instead of classical normal distribution, is rising up in many statistical theories and applications. In this paper, we deal with saddlepoint approximation for the distribution function of sample mean of skew-normal distribution. Comparing to normal approximation, saddlepoint approximation provides very accurate results in small sample sizes as well as for large or moderate sample sizes. Saddlepoint approximations related to the skew-normal distribution, suggested in this paper, can be used as a approximate approach to the classical method of Gupta and Chen (2001) and Chen et al. (2004) which need very complicate calculations. Through simulation study, we verified the accuracy of the suggested approximation and applied the approximation to Robert's (1966) twin data.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.679-686
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• 2007

Moment expressions are derived for the internally truncated normal distributions commonly applied to screening and constrained problems. They are obtained from using a recursive relation between the moments of the normal distribution whose distribution is truncated in its internal part. Closed form formulae for the moments can be presented up to $N^{th}$ order under the internally truncated case. Necessary theories and two applications are provided.

• Journal of the Korea Institute of Military Science and Technology
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• v.24 no.4
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• pp.401-407
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• 2021

To confirm the change of muzzle velocity and the most suitable probability distribution model of the 155 mm K9 howitzer barrel with chrome plating and changed rifling. Using a statistical program, the muzzle velocity were plotted on a normal distribution, a 2-parameter and 3-parameter Weibull distribution on a probability paper. Also, statistical parameters were estimated and muzzle velocity fitness test and probability of K676 charge were plotted. In both the chrome-plated with standard rifling and changed rifling for K9 barrel, the 2-parameter and 3-parameter Weibull distribution were skewed to the left compared to the normal distribution. It was confirmed that the muzzle velocity of the K9 barrel with chromium-plated is suitable for the normal distribution and 3-parameter Weibull distribution model.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1267-1276
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• 2009

This paper presents a method for approximation of the standard normal distribution by using hyperbolic tangent based functions. The presented approximate formula for the cumulative distribution depends on one numerical coefficient only, and its accuracy is admissible. Furthermore, in some particular cases, closed forms of inverse formulas are derived. Numerical results of the present method are compared with those of an existing method.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.261-265
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• 2017

Let X and Y be independent identically distributed nondegenerate random variables with common absolutely continuous probability distribution function F(x) and the corresponding probability density function f(x) and $E(X^2)$<${\infty}$. Put Z = max(X, Y) and W = min(X, Y). In this paper, it is proved that Z - W and Z + W or$(X-Y)^2$ and X + Y are independent if and only if X and Y have normal distribution.

• Journal of the Korean Data and Information Science Society
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• v.21 no.2
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• pp.241-250
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• 2010

Over the past few decades, several studies have been made on the modeling of circular data. But these studies focused mainly on the symmetrical cases including von Mises distribution. Recently, many studies with skew-normal distribution have been conducted in the linear case. In this paper, we dealt the problem of fitting of non-symmetrical circular data with wrapped skew-normal distribution which can be derived by using the principle of wrapping. Wrapped skew-normal distribution is very flexible to asymmetical data as well as to symmetrical data. Multi-modal data are also fitted by using the mixture of wrapped skew-normal distributions. To estimate the parameters of mixture, we suggested the EM algorithm. Finally we verified the accuracy of the suggested algorithm through simulation studies. Application with real data is also considered.