• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.243-247
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• 2014

Let {$X_n$, $n{\geq}1$} be a sequence of i.i.d. random variables with absolutely continuous cumulative distribution function(cdf) F(x) and the corresponding probability density function(pdf) f(x). In this paper, we give characterizations of Pareto and Weibull distribution by considering conditional expectations of record values.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.149-153
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• 2009

Let {$X_{n},\;n\;\geq\;1$} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f(x). Suppose $X_{U(m)},\;m = 1,\;2,\;{\cdots}$ be the upper record values of {$X_{n},\;n\;\geq\;1$}. It is shown that the linearity of the conditional expectation of $X_{U(n+2)}$ given $X_{U(n)}$ characterizes the lomax, exponential and pareto distributions.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.363-374
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• 2006

A new bivariate beta distribution based on the Appell function of the third kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure as well as the Fisher information matrix.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.441-446
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• 2003

Let { $X_{n}$ , n $\geq$ 1} be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function f(x). Let $Y_{n}$ = max{ $X_1$, $X_2$, …, $X_{n}$ } for n $\geq$ 1. We say $X_{j}$ is an upper record value of { $X_{n}$ , n$\geq$1} if $Y_{j}$ > $Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, n$\geq$1, where u(n) = min{j｜j>u(n-1), $X_{j}$ > $X_{u}$ (n-1), n$\geq$2} and u(1) = 1. We call the random variable X $\in$ Beta (1, c) if the corresponding probability cumulative function F(x) of x is of the form F(x) = 1-(1-x)$^{c}$ , c>0, 0$\leq$x$\leq$1. In this paper, we will give a characterization of the beta distribution of the first kind by considering conditional expectations of record values.s.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.309-316
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• 2007

In this paper, we decompose the whole likelihood based on grouped data into conditional likelihoods and study the approximate contribution of additional inspection to the efficiency. We also combine the conditional maximum likelihood estimators to construct an approximate maximum likelihood estimator. For an exponential distribution, we see that a large inspection size does not increase the efficiency much if the failure rate is small, and the maximum likelihood estimator can be approximated with a linear function of inspection times.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.385-396
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• 2016

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics.

• Journal of Korean Institute of Industrial Engineers
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• v.41 no.1
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• pp.10-16
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• 2015

In this study, we suggest a method to predict probability distribution of a new customer's degree of loyalty using C-CRF that reflects the RFM score and similarity to the neighbors of the customer. An RFM score prediction model is introduced to construct the first feature function of C-CRF. Integrating demographical similarity, purchasing characteristic similarity and purchase history similarity, we make a unified similarity variable to configure the second feature function of C-CRF. Then parameters of each feature function are estimated and we train our C-CRF model by training data set and suggest a probabilistic distribution to estimate a new customer's degree of loyalty. An example is provided to illustrate our model.

• Journal of Electrical Engineering and Technology
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• v.11 no.6
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• pp.1872-1879
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• 2016

The techniques to recycle and reuse plastics attract public attention. These public attraction and needs result in improving the recycling technique. However, the identification technique for black plastic wastes still have big problem that the spectrum extracted from near infrared radiation spectroscopy is not clear and is contaminated by noise. To overcome this problem, we apply Raman spectroscopy to extract a clear spectrum of plastic material. In addition, to improve the classification ability of fuzzy Radial Basis Function Neural Networks, we apply supervised learning based clustering method instead of unsupervised clustering method. The conditional fuzzy C-Means clustering method, which is a kind of supervised learning based clustering algorithms, is used to determine the location of radial basis functions. The conditional fuzzy C-Means clustering analyzes the data distribution over input space under the supervision of auxiliary information. The auxiliary information is defined by using k Nearest Neighbor approach.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.1-15
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• 2014

A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.

• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.975-982
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• 2003

In this paper we considered the problem of estimating the bivariate survival distribution of the random vector (X, Y) when Y may be subject to random censoring but X is always uncensored. Adapting conditional Koziol-Green model, simplified estimator for bivariate survival function is proposed. We perform simulation to compare the proposed estimator with popular estimators and discussed the performance of it.