• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.305-310
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• 1998

In this paper, we introduce the conditions that the P-process has the intensity function which it is a standard form of gamma distribution. And we show that the transformed geometric Poisson process which the intensity function is a standard form of gamma distribution is a alternative sign P-process

• Journal of the Optical Society of Korea
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• v.19 no.3
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• pp.237-240
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• 2015

We derived the average bit error rate (BER) of coherent free-space optical (FSO) systems with digital binary phase shift keying (BPSK) modulations over atmospheric turbulence channels with a gamma-gamma distribution. To obtain a generalized derivation in a closed-form expression, we used special integrals and transformations of the Meijer G function. Furthermore, we numerically analyzed and simulated the average BER behavior according to the average SNR for different turbulence strengths. Simulation results are demonstrated to confirm the analytical results.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.411-418
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• 2007

Let $X_1$, ${\cdots}$, $X_n$ be nondegenerate and positive independent identically distributed(i.i.d.) random variables with common absolutely continuous distribution function F(x) and $E(X^2)$ < ${\infty}$. The random variables $X_1+{\cdots}+X_n$ and $\frac{X_1+{\cdots}+X_m}{X_1+{\cdots}+X_n}$are independent for 1 $1{\leq}$ m < n if and only if $X_1$, ${\cdots}$, $X_n$ have gamma distribution.

• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.219-223
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• 2009

We shall derive a quotient distribution of two independent gamma variables and its moment and reliability are represented by hypergeometric function and Wittaker's function. And we shall consider an inference on the reliability in two independent gamma random variables.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.101-113
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• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.875-888
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• 2017

The Rayleigh distribution has been commonly used in life time testing studies of the probability of surviving until mission time. We focus on a reliability function of the Rayleigh distribution and deal with prior distribution on R(t). This paper is an effort to obtain Bayes estimators of rayleigh distribution with three different prior distribution on the reliability function; a noninformative prior, uniform prior and inverse gamma prior. We have found the Bayes estimator and predictive density function of a future observation y with each prior distribution. We compare the performance of the Bayes estimators under different sample size and in simulation study. We also derive the most plausible region, prediction intervals for a future observation.

• Water for future
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• v.26 no.4
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• pp.73-83
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• 1993

This study focuses on the separation effect analysis of rainfall data for 2-parameter log-normal, 3-parameter log-normal, type-extreme value, 2-parameter gamma, 3-parameter gamma, log-Pearson type-III, and general extreme value distribution functions. Difference in the relationship between the mean and standard deviation of skewness for historical data and relations derived from 7 distribution functions are analyzed suing the Monte Carlo experiment. The results show that rainfall data has the separation effect for 6 distribution functions except 3-parameter gamma distribution function.

• International Journal of Reliability and Applications
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• v.15 no.2
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• pp.111-123
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• 2014

A new class of bivariate distributions is derived by specifying its conditionals as the exponential and gamma distributions. Some properties and relations with other distributions of the new class are studied. In particular, the estimation of parameters is considered by the methods of maximum likelihood and pseudolikelihood of a special case of the new class. An application using a real bivariate data is given for illustrating the flexibility of the new class in this context, and, also, for comparing the estimation results obtained by the maximum likelihood and pseudolikelihood methods.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1563-1575
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• 2018

In this paper, our central focus is upon gamma and beta q-distributions from a probabilistic viewpoint. The gamma and the beta q-distributions are characterized by investing the nature of the joint q-probability density function through the q-independence property and the q-Laplace transform.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.71-80
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• 2007

The present paper investigates estimation of a scale parameter of a gamma distribution using a loss function that reflects both goodness of fit and precision of estimation. The Bayes and empirical Bayes estimators rotative to balanced loss functions (BLFs) are derived and optimality of some estimators are studied.