• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.105-121
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• 2019

One of the main objective of manufacturing industries is to assess the capability performance of different processes. In this paper, we use the lifetime performance index $C_L$ as a criterion to measure larger-the-better type quality characteristic for evaluating the product performance. The lifetimes of products are assumed to follow a general class of inverted exponentiated distributions. We use maximum likelihood estimator to estimate the lifetime performance index under the assumption that data are progressive type I interval censored. We also obtain asymptotic distribution of this estimator. Based on this estimator, a new hypothesis testing procedure is developed with respect to a given lower specification limit. Finally, two numerical examples are discussed in support of the proposed testing procedure.

• Journal of the Korean Society of Clothing and Textiles
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• v.23 no.2
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• pp.185-195
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• 1999

The purpose of this study is to identify store image and clothing satisfaction of various clothing distribution type and is to compare the difference due to demographic variables. The data were obtained 407 housewives using questionnaire. The results were as follows. First Store image of clothing distribution types was found significant differences in product service atmosphere. Second Clothing satisfaction of clothing distribution types was founded significant differences in price brand name fashion design material sewing size. Third The new distribution types in general were not visited upon despite their high degree of recognition and using experience of new distribution types was founded significant differences in Store image of new distribution types. Fourth Among demographic variables significant difference in usage of the distributions was founded. Fifth Among demographic variables significant difference in usage of the distributions was founded. Fifth Among demographic variables significant difference in clothing satisfaction of the distributions was founded.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1157-1169
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• 2016

We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.583-592
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• 2007

Given the moments of a symmetric random variable, its density and distribution functions can be accurately approximated by making use of the algorithm proposed in this paper. This algorithm is specially designed for approximating symmetric distributions and comprises of four phases. This approach is essentially based on the transformation of variable technique and moment-based density approximants expressed in terms of the product of an appropriate initial approximant and a polynomial adjustment. Probabilistic quantities such as percentage points and percentiles can also be accurately determined from approximation of the corresponding distribution functions. This algorithm is not only conceptually simple but also easy to implement. As illustrated by the first two numerical examples, the density functions so obtained are in good agreement with the exact values. Moreover, the proposed approximation algorithm can provide the more accurate quantities than direct approximation as shown in the last example.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.517-530
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• 2015

In this paper, we establish a class of strong limit theorems, represented by inequalities, for the arbitrary random field with respect to the product binomial distributions indexed by the infinite tree on the generalized random selection system by constructing the consistent distri-bution and a nonnegative martingale with pure analytical methods. As corollaries, some limit properties for the Markov chain field with respect to the binomial distributions indexed by the infinite tree on the generalized random selection system are studied.

• The Korean Journal of Applied Statistics
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• v.30 no.3
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• pp.363-376
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• 2017

The insurance market is saturated and its growth engine is exhausted; consequently, the insurance industry is now in a low growth period with insurance companies that face a fierce competitive environment. In such a situation, it will be an important issue to find the probability distributions that can explain the flow of insurance claims, which are the basis of the actuarial calculation of the insurance product. Insurance claims are generally known to be well fitted by lognormal distributions or Pareto distributions biased to the left with a thick tail. In recent years, skew normal distributions or skew t distributions have been considered reasonable distributions for describing insurance claims. Cooray and Ananda (2005) proposed a composite lognormal-Pareto distribution that has the advantages of both lognormal and Pareto distributions and they also showed the composite distribution has a higher fitness than single distributions. In this paper, we introduce new composite distributions based on skew normal distributions or skew t distributions and apply them to Danish fire insurance claim data and US indemnity loss data to compare their performance with the other composite distributions and single distributions.

• Journal of KIISE:Software and Applications
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• v.27 no.8
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• pp.855-863
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• 2000

Although Behavior-Knowledge Space (BKS) method, one of well known decision combination methods, does not need any assumptions in combining the multiple experts, it should theoretically build exponential storage spaces for storing and managing jointly observed K decisions from K experts. That is, combining K experts needs a (K+1)st-order probability distribution. However, it is well known that the distribution becomes unmanageable in storing and estimating, even for a small K. In order to overcome such weakness, it has been studied to decompose a probability distribution into a number of component distributions and to approximate the distribution with a product of the component distributions. One of such previous works is to apply a conditional independence assumption to the distribution. Another work is to approximate the distribution with a product of only first-order tree dependencies or second-order distributions as shown in [1]. In this paper, higher order dependency than the first-order is considered in approximating the distribution and a dependency-based framework is proposed to optimally approximate the (K+1)st-order probability distribution with a product set of dth-order dependencies where ($1{\le}d{\le}K$), and to combine multiple experts based on the product set using the Bayesian formalism. This framework was experimented and evaluated with a standardized CENPARMI data base.

• Journal of Environmental Health Sciences
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• v.48 no.5
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• pp.266-271
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• 2022

Background: The selection of distributions of input parameters is an important component in probabilistic exposure assessment. Goodness-of-fit (GOF) methods are used to determine the distribution of exposure factors. However, there are no clear guidelines for choosing an appropriate GOF method. Objectives: The outcomes of probabilistic consumer exposure assessment were compared by using five different GOF methods for the selection of input distributions: chi-squared test, Kolmogorov-Smirnov test (K-S), Anderson-Darling test (A-D), Akaike information criterion (AIC) and Bayesian information criterion (BIC). Methods: Individual exposures were estimated based on product usage factor combinations from 10,000 respondents. The distribution of individual exposure was considered as the true value of population exposures. Results: Among the five GOF methods, probabilistic exposure distributions using the A-D and K-S methods were similar to individual exposure estimations. Comparing the 95th percentiles of the probabilistic distributions and the individual estimations for 10 CPs, there were 0.73 to 1.92 times differences for the A-D method, and 0.73 to 1.60 times differences (excluding tire-shine spray) for the K-S method. Conclusions: There were significant differences in exposure assessment results among the selection of the GOF methods. Therefore, the GOF methods for probabilistic consumer exposure assessment should be carefully selected.

• Journal of Industrial Technology
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• v.3
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• pp.39-46
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• 1983

This paper presents a quantitative measure of the degree of part commonality and redundancy in a product line based on entropy measure of information theory. The several possible methods of analysis are discussed and the use of the entropy measure is discussed. These commonality and redundancy measure can be applied to analyze the usage pattern of part across a product line and to determine which parts have the broadest usage across the firm's product lines. An analysis of the results by entropy statistics is compared with the practical part usage in a simulation of several types of part usage's distributions.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.519-531
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• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.