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Reliability and ratio in exponentiated complementary power function distribution
Yeung Gil Moon,Chang Soo Lee,Se Gi Ryu 한국데이터정보과학회 2009 한국데이터정보과학회지 Vol.20 No.5
As we shall define an exponentiated complementary power function distribution, we shall consider moments, hazard rate, and inference for parameter in the distribution. And we shall consider an inference of the reliability and distributions for the quotient and the ratio in two independent exponentiated complementary power function random variables.
Estimating exponentiated parameter and distribution of quotient and ratio in an exponentiated Pareto
Moon, Yeung-Gil,Lee, Chang-Soo,Kang, Jun-Ho The Korean Data and Information Science Society 2010 한국데이터정보과학회지 Vol.21 No.5
We shall consider estimations of an exponetiated parameter of the exponentiated Pareto distribution with known scale and threshold parameters. A quotient distribution of two independent exponentiated Pareto random variables is obtained. We also derive the distribution of the ratio of two independent exponentiated Pareto random variables.
Inference on the reliability P(Y < X) in the gamma case
Moon, Yeung-Gil,Lee, Chang-Soo The Korean Data and Information Science Society 2009 한국데이터정보과학회지 Vol.20 No.1
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.
Estimating reliability in discrete distributions
Yeung Gil Moon,Chang Soo Lee 한국데이터정보과학회 2011 한국데이터정보과학회지 Vol.22 No.4
We shall introduce a general probability mass function which includes several discrete probability mass functions. Especially, when the random variable X is Poisson, binomial, and negative binomial random variables as some special cases of the in-troduced distribution, the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the probability P(X ≤ t) are considered. And the efficiencies of the MLE and the UMVUE of the reliability are compared each other.
Estimating reliability in discrete distributions
Moon, Yeung-Gil,Lee, Chang-Soo The Korean Data and Information Science Society 2011 한국데이터정보과학회지 Vol.22 No.4
We shall introduce a general probability mass function which includes several discrete probability mass functions. Especially, when the random variable X is Poisson, binomial, and negative binomial random variables as some special cases of the introduced distribution, the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the probability P(X ${\leq}$ t) are considered. And the efficiencies of the MLE and the UMVUE of the reliability ar compared each other.
Reliability and ratio in exponentiated complementary power function distribution
Moon, Yeung-Gil,Lee, Chang-Soo,Ryu, Se-Gi The Korean Data and Information Science Society 2009 한국데이터정보과학회지 Vol.20 No.5
As we shall dene an exponentiated complementary power function distribution, we shall consider moments, hazard rate, and inference for parameter in the distribution. And we shall consider an inference of the reliability and distributions for the quotient and the ratio in two independent exponentiated complementary power function random variables.
Estimating exponentiated parameter and distribution of quotient and ratio in an exponentiated Pareto
Yeung Gil Moon,Chang Soo Lee,Jun Ho Kang 한국데이터정보과학회 2010 한국데이터정보과학회지 Vol.21 No.5
We shall consider estimations of an exponetiated parameter of the exponentiated Pareto distribution with known scale and threshold parameters. A quotient distribution of two independent exponentiated Pareto random variables is obtained. We also derive the distribution of the ratio of two independent exponentiated Pareto random variables.
Reliability estimation and ratio distribution in a general exponential distribution
Lee, Chang-Soo,Moon, Yeung-Gil The Korean Data and Information Science Society 2014 한국데이터정보과학회지 Vol.25 No.3
We shall consider the estimation for the parameter and the right tail probability in a general exponential distribution. We also shall consider the estimation of the reliability P(X < Y ) and the skewness trends of the density function of the ratio X=(X+Y) for two independent general exponential variables each having different shape parameters and known scale parameter. We then shall consider the estimation of the failure rate average and the hazard function for a general exponential variable having the density function with the unknown shape and known scale parameters, and for a bivariate density induced by the general exponential density.
On the maximum and minimum in a bivariate uniform distribution
Changsoo Lee,Hyejung Shin,Yeung Gil Moon 한국데이터정보과학회 2015 한국데이터정보과학회지 Vol.26 No.6
We obtain means and variances of max {X, Y} and min {X, Y} in the underlying Morgenstern type bivariate uniform variables X and Y with same scale parameters and different scale parameters respectively. And we obtain the conditional expectations in the underlying Morgenstern type bivariate uniform variables. Here, we shall consider the conditional expectations to know the dependence of one variable on the other variable and we consider the behaviors of means and variances ofmax {X, Y} and min {X, Y} with respect to changes in means, variances, and the correlation coefficient of the underlying Morgenstern type bivariate uniform variables.