• Advances in Computational Design
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• v.7 no.1
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• pp.37-56
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• 2022

Phase-type distributions are the distributions of the time to absorption in finite and absorbing Markov chains. They generalize, while at the same time, retain the tractability of the exponential distributions and their family. They are widely used as stochastic models from queuing theory, reliability, dependability, and forecasting, to computer networks, security, and computational design. The ability to fit phase-type distributions to intractable or empirical distributions is, therefore, highly desirable for many practical purposes. Many methods and tools currently exist for this fitting problem. In this paper, we present the results of our investigation on using orthogonal-distance fitting as a method for fitting phase-type distributions, together with a comparison to the currently existing fitting methods and tools.

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.205-220
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• 2009

For modeling skewed semicircular data, we derive new family of the exponential distributions. We extend it to the l-axial exponential distribution by a transformation for modeling any arc of arbitrary length. It is straightforward to generate samples from the f-axial exponential distribution. Asymptotic result reveals two things. The first is that linear exponential distribution can be used to approximate the l-axial exponential distribution. The second is that the l-axial exponential distribution has the asymptotic memoryless property though it doesn't have strict memoryless property. Some trigonometric moments are also derived in closed forms. Maximum likelihood estimation is adopted to estimate model parameters. Some hypotheses tests and confidence intervals are also developed. The Kolmogorov-Smirnov test is adopted for goodness of fit test of the l-axial exponential distribution. We finally obtain a bivariate version of two kinds of the l-axial exponential distributions.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1033-1047
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• 2009

In this paper, we consider a m-type risk model with Markov-modulated premium rate. A integral equation for the conditional ruin probability is obtained. A recursive inequality for the ruin probability with the stationary initial distribution and the upper bound for the ruin probability with no initial reserve are given. A system of Laplace transforms of non-ruin probabilities, given the initial environment state, is established from a system of integro-differential equations. In the two-state model, explicit formulas for non-ruin probabilities are obtained when the initial reserve is zero or when both claim size distributions belong to the $K_n$-family, n $\in$ $N^+$ One example is given with claim sizes that have exponential distributions.

• Journal of the Korean Data and Information Science Society
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• v.22 no.1
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• pp.29-35
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• 2011

In statistical process control, the primary method used to monitor the number of nonconformities is the c-chart. The conventional c-chart is based on the assumption that the occurrence of nonconformities in samples is well modeled by a Poisson distribution. When the Poisson assumption is not met, the X-chart is often used as an alternative charting scheme in practice. And CUSUM-chart is used when it is desirable to detect out of control situations very quickly because of sensitive to a small or gradual drift in the process. In this paper, I compare CUSUM-chart to X-chart for the Katz family covering equi-, under-, and over-dispersed distributions relative to the Poisson distribution.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.875-883
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• 2001

We derive the asymptotic relative efficiencies in two special cases of Chaudhuri's estimators for the multivariate one sample problem. And we compare those two when observations are independent and identically distributed from a family of spherically symmetric distributions including normal distributions.

• Communications for Statistical Applications and Methods
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• v.24 no.1
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• pp.43-65
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• 2017

We propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest has the Poisson distribution and the time for the event follows the gamma-G family of distributions. The extended family of gamma-G failure-time models with long-term survivors is flexible enough to include many commonly used failure-time distributions as special cases. We consider a frequentist analysis for parameter estimation and derive appropriate matrices to assess local influence on the parameters. Further, various simulations are performed for different parameter settings, sample sizes and censoring percentages. We illustrate the performance of the proposed regression model by means of a data set from the medical area (gastric cancer).

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.85-95
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• 2012

In this paper we define extended negative quadrant dependence which is weaker negative quadrant dependence and show conditions for having extended negative quadrant dependence property. We also derive generalized Farlie-Gumbel-Morgenstern uniform distributions that possess the extended quadrant dependence property.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.245-249
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• 2019

In this paper we obtain characterizations of a family of continuous probability distribution by independence property of upper record values. Also, we introduce some examples of the characterizations of distributions from these general classes of continuous distributions.

• Journal of the Korean Statistical Society
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• v.29 no.3
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• pp.315-318
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• 2000

In this note we use the Poisson Summation Formula to generalize a result of Harris and Park (1994) on lattice distributions induced by uniform (0,1) random variables to those generated by random variables with step functions as their probability functions.

• Journal of the Korean Statistical Society
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• v.20 no.1
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• pp.57-66
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• 1991

This paper deals with the problem of estimating an arbitrary piecewise continuous function of the parameter under squared error loss in the one parameter exponential family. Using Blyth's(1951) method sufficient conditions are given for the admissibility of (possibly generalized Bayes) estimators. Also, some examples are provided for normal, binomial, and gamma distributions.