• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.265-274
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• 2004

The paper extends earlier work on the skew-normal distribution, a family of distributions including normal, but with extra parameter to regulate skewness. The present work introduces a singly truncated parametric family that strictly includes a truncated normal distribution, and studies its properties, with special emphasis on the relation with bivariate normal distribution.

• 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.

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.255-266
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• 2006

This paper proposes a class of distributions which is useful in making inferences about the sum of values from a normal and a doubly truncated normal distribution. It is seen that the class is associated with the conditional distributions of truncated bivariate normal. The salient features of the class are mathematical tractability and strict inclusion of the normal and the skew-normal laws. Further it includes a shape parameter, to some extent, controls the index of skewness so that the class of distributions will prove useful in other contexts. Necessary theories involved in deriving the class of distributions are provided and some properties of the class are also studied.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.879-885
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• 1998

In this paper, we propose the approximate maximum likelihood estimators (AMLE) of the location and the scale parameter of the singly left truncated normal distribution. We compare the proposed estimators with the simpler estimators (SE) in terms of the mean squared error (MSE) through Monte Carlo methods.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.17 no.4
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• pp.221-231
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• 2005

The present study is deeply concerned with the reliability design method(Level III) for caisson breakwaters using expected sliding distance, and the objectives of this study are to propose the employment of a doubly-truncated normal distribution and to present the validity for it. In this study, therefore, the explanations are made for consideration of effects of uncertain factors, and a clear basis that the doubly-truncated normal distribution should be employed in the computation process of expected sliding distance by Monte-Carlo simulation is presented with introduction of the employment method. Even though only caisson breakwaters are treated in this paper, the employment of doubly-truncated normal distribution can be applied to various coastal structures as well as other engineering fields, and therefore it is expected that the present study will be extended in various fields.

• Journal of the Korean Statistical Society
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• v.34 no.3
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• pp.245-261
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• 2005

The marginal distribution of X is considered when (X, Y) has a truncated bivariate t-distribution. This paper mainly focuses on the marginal nontruncated distribution of X where Y is truncated below at its mean and its observations are not available. Several properties and applications of this distribution, including relationship with Azzalini's skew-normal distribution, are obtained. To circumvent inferential problem arises from adopting the frequentist's approach, a Bayesian method utilizing a data augmentation method is suggested. Illustrative examples demonstrate the performance of the method.

• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.377-383
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• 2020

The likelihood-based inference in a nonlinear generalized mixed model often requires computing moments of truncated multivariate normal random variables. Many methods have been proposed for the computation using a recurrence relation or the moment generating function; however, these methods rely on high dimensional numerical integrations. The numerical method is known to be inefficient for high dimensional integral in accuracy. Besides the accuracy, the methods demand too much computing time to use them in practical analyses. In this note, a moment calculation method is proposed under an assumption of a certain covariance structure that occurred mostly in generalized mixed models. The method needs only low dimensional numerical integrations.

• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.673-679
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• 2021

The moment calculation in a truncated multivariate normal distribution is a long-standing problem in statistical computation. Recently, Kan and Robotti (2017) developed an algorithm able to calculate all orders of moment under different types of truncation. This result was implemented in an R package MomTrunc by Galarza et al. (2021); however, it is difficult to use the package in practical statistical problems because the computational burden increases exponentially as the order of the moment or the dimension of the random vector increases. Meanwhile, Lee (2021) presented an efficient numerical method in both accuracy and computational burden using Gauss-Hermit quadrature. This article introduces trunmnt implementation of Lee's work as an R package. The Package is believed to be useful for moment calculations in most practical statistical problems.

• Communications for Statistical Applications and Methods
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• v.21 no.5
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• pp.461-469
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• 2014

Characteristic functions play an important role in probability and statistics; however, a rigorous derivation of these functions requires contour integration, which is unfamiliar to most statistics students. Without resorting to contour integration, Datta and Ghosh (2007) derived the characteristic functions of normal, Cauchy, and double exponential distributions. Here, we derive the characteristic functions of t, truncated normal, skew-normal, and skew-t distributions. The characteristic functions of normal, cauchy distributions are obtained as a byproduct. The derivations are straightforward and can be presented in statistics masters theory classes.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.249-259
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• 2002

In order to estimate the mean and variance for a Normal distribution which is truncated at both right and left sides, maximum likelihood estimators based on the entire sample from the original distribution are compared with the sample mean and variance of the censored sample which is the data remaining after truncation using simulation. We found that, surprisingly, the mean squared error of the mean based on the censored data Is smaller than that of the full sample estimators.