• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.471-477
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• 2007

In this paper we establish some recurrence relations satisfied by the quotient moments of the upper record values from the Weibull distribution. Suppose $X{\in}WEI({\lambda})\;then\;E(\frac {X^\tau_U(m)} {X^{s+1}_{U(n)}})=\frac{1}{(s-\lambda+1)}E(\frac {X^\tau_U(m)}{X^{s-\lambda+1}_{U(n-1)}})-\frac{1}{(s-\lambda+1)}+E(\frac{X^\tau_U(m)}{X^{s-\lambda+1}_{U(n)}})\;and\;E(\frac {X^{\tau+1}_{U(m)}}{X^s_{U(n)}})=\frac{1}{(r+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m)}}{X^s_{U(n-1)}})-\frac{1}{(\tau+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m-1)}}{X^s_{U(n-1)}})$.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.51-57
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• 2007

In this paper, we establish characterizations of the Pareto distribution by the independence of record values. We prove that $X{\in}PAR(1,{\beta})$ for ${\beta}$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(n)}-X_{U(n+1)}}$ and $X_{U(n)}$ are independent for $n{\geq}1$. And we show that $X{\in}PAR(1,{\beta})$ for ${\beta}$ > 0, if and only if $\frac{X_{U(n)}-X_{U(n+1)}}{X_{U(n)}}$ and $X_{U(n)}$ are independent for $n{\geq}1$.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.163-167
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• 2008

This paper presents characterizations of the Weibull distribution by the independence of record values. We prove that $X\;{\in}\;W\;EI ({\alpha})$, if and only if $\frac {X_{U(n+l)}} {X_{U(n+1)}\;+\;X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent or $\frac {X_{U(n)}} {X_{U(n+1)}\;+\;X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent. And also we establish that $X\;{\in}\;W\;EI({\alpha})$, if and only if $\frac {X_{U(n+1)}\;-\;X_{U(n)}} {X_{U(n+1)}\;+\;X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.127-131
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• 2003

Let X$_1$, X$_2$,... be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X$_j$ is an upper record value of this sequence if X$_j$ > max {X$_1$,X$_2$,...,X$_{j-1}$}. We define u(n)=min{j$\mid$j> u(n-1), X$_j$ > X$_{u(n-1)}$, n $\geq$ 2} with u(1)=1. Then F(x) = 1-x$^{\theta}$, x > 1, ${\theta}$ < -1 if and only if (${\theta}$+1)E[X$_{u(n+1)}$$\mid$X$_{u(m)}$=y] = ${\theta}E[X_{u(n)}$\mid$X_{u(m)}=y], (\theta+1)^2E[X_{u(n+2)}$\mid$X_{u(m)}=y] = \theta^2E[X_{u(n)}$\mid$X_{u(m)}=y], or (\theta+1)^3E[X_{u(n+3)}$\mid$X_{u(m)}=y] = \theta^3E[X_{u(n)}$\mid$X_{u(m)}=y], n $\geq$ M+1$.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.477-493
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• 2017

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random variables like order statistics and lower record values. With this definition we give simple expressions for single and product moments of dual generalized order statistics from Dagum distribution. The results for order statistics and lower records are deduced from the relations derived and some computational works are also carried out. Further, a characterizing result of this distribution on using the conditional moment of the dual generalized order statistics is discussed. These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we tabulate the means, variances, skewness and kurtosis of order statistics and record values of the Dagum distribution.

• Fisheries and Aquatic Sciences
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• v.16 no.1
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• pp.53-56
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• 2013

A pagurid hermit crab, Pagurus rathbuni that was collected from the deep water of the East Sea, Korea, has been newly recorded in the Korean fauna. The present record extends the geographic distribution of the species to Korean waters in the East Sea and extends the bathymetric range to 500 m. Morphological and distributional accounts of this species are presented with illustrations.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.485-489
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• 2010

A family of continuous probability distribution has been characterized through the difference of two conditional expectations, conditioned on a non-adjacent record statistic. Also, a result based on the unconditional expectation and a conditional expectation is used to characterize a family of distributions. Further, some of its deductions are also discussed.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.821-829
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• 2023

In this paper, we obtain characterizations of continuous distributions based on the independent property of generalized record values extending the characterization results reported by Jin and Lee [4], Skřivánková and Juhás [8]. Also, example of special cases of general classes as Bur types, Pareto, power and Weibull distribution are discussed.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.53 no.6
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• pp.316-323
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• 2004

This paper develops an ADWHM(Advanced Digital Watt-Hour Meter) which integrates and implements the voltage management data record function and the load management data record function in the electronic watt-hour meter. ADWHM is developed based on PIC16F874 which is 8bit micro-controller of RISK type for the easy of programing and maintenance, and electronic power signal processing module is located at front of it to reduce the computing load of processor. Also, a 16kbyte EEPROM is used to record the voltage management data and load management data for a week as well as watt-hour data and USART communication mode is used to transfer data from ADWHM to PC. The accuracy of the voltage and unt measuring for ADWHM is verified by identifying the LCD display values of the ADWHM after the voltage signals of id levels from digital function generator is applied to PT(Potential Transformer) and CT(Current Transformer) output under state which it is separated from real power line. On the its basic functions such as watt-hour data recording function, voltage management data recording function and load management data recording function was verified by showing data for three days among the collected data to PC by RS232C communication from ADWHM which was connected to real power lines for a week.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.347-361
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• 2014

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distribution includes exponential distribution, Pareto or Lomax distribution. In this paper, we established exact expressions and recurrence relations satised by the quotient moments of generalized order statistics for a generalized Pareto distribution. Further the results for quotient moments of order statistics and records are deduced from the relations obtained and a theorem for characterizing this distribution is presented.