• Kyungpook Mathematical Journal
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• 제48권3호
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• pp.411-417
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• 2008

In the present paper we derive the distribution of single order statistics, joint distribution of two order statistics and the distribution of product and quotient of two order statistics when the independent random variables are from continuous Kumaraswamy distribution. In particular the distribution of product and quotient of extreme order statistics and consecutive order statistics have also been obtained. The method used is based on Mellin transform and its inverse.

• Journal of the Korean Statistical Society
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• 제28권3호
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• pp.279-296
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• 1999

In this paper we establish some recurrence relations for both single and product moments of order statistics from a doubly truncated linear- exponential distribution with increasing hazard rate. These recurrence relations would enable one to compute all the higher order moments of order statistics for all sample sizes from those of the lower order in a simple recursive way. In addition, percentage points of order statistics are also discussed. These generalize the corresponding results for the linear- exponential distribution with increasing hazard rate derived by Balakrishnan and Malik(1986)

• 충청수학회지
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• 제27권3호
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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.

• Communications for Statistical Applications and Methods
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• 제18권4호
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• pp.485-493
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• 2011

The proportional likelihood ratio order is an extension of the likelihood ratio order for the non-negative absolutely continuous random variables. In addition, the Lindley distribution has been over looked as a mixture of two exponential distributions due to the popularity of the exponential distribution. In this paper, we first recalled the above concepts and then obtained various properties of the Lindley distribution due to the proportional likelihood ratio order. These results are more general than the likelihood ratio ordering aspects related to this distribution. Finally, we discussed the proportional likelihood ratio ordering in view of the weighted version of the Lindley distribution.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.243-250
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• 1999

We consider $Y=X{\lambda}Z,\;{\lambda}>0$, where X and Z are independent random variables, and Y is the length biased distribution or the equilibrium distribution of X. The purpose of this paper is to consider the distribution of X or Y when the distribution of Z is given and the distribution of Z when the distribution of X or Y is given, In particular, we obtain that the necessary and sufficient conditions for X to be $X^{2}({\upsilon})\;is\;Z{\sim}X^{2}(2)\;and\;for\;Z\;to\;be\;X^{2}(1)\;is\;X{\sim}IG({\mu},\;{\mu}^{2}/{\lambda})$, where $IG({\mu},\;{\mu}^{2}/{\lambda})$ is two-parameter inverse Gaussian distribution. Also we show that X is smaller than Y in the reverse Laplace transform ratio order if and only if $X_{e}$ is smaller than $Y_{e}$ in the Laplace transform ratio order. Finally, we can get the results that if X is smaller than Y in the Laplace transform ratio order, then $Y_{L}$ is smaller than $X_{L}$ in the Laplace transform order, and that if X is smaller than Y in the reverse Laplace transform ratio order, then $_{\mu}X_{L}$ is smaller than $_{\nu}Y_{L}$ in the Laplace transform order.

• 대한한의학회지
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• 제17권2호
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• pp.318-330
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• 1996

We had been investigated the effect of ear acupuncture in alcoholics, but in Kang won do province never we have been investigated. so then in Sangji university oriental hospital from Mar. 1. 1995 to Feb. 28. 1996. we clinically analized 102 alcoholics treated The results were summarized as follow: 1. In Age distribution, 40s were the top as 28.4% and next 30s, 50s, 60s 70s, below 3Os. In Sex distribution, these were 92 person in male, 10 person in female. 2. Marrige Status revealed in descending order ; married, single, divorced Sibling order distribution in descending order; eldest son, middle son, youngest son, only son 3. Distribution of education in descending order ; high school, middle school, primary school, collage and graduate school, illiterate 4. Distribution of occupation in descending order; farmer, labor, merchent, salaried and inoccupation, service 5. Distribution of religion in descending order ; none, buddism, protestantism, catholicism 6. Distribution of family history of alcoholism; yes(24.5%), no(69.6%) 7. Distribution of onset of drinking in descending order ; 20s, below 20s, 30s and 40s, 50s 8. Distribution of duration of drinking in descending order ; 20-29 years, 10-19 and below years, 40-49 years, 30-39 years 9. Distribution of the reason of drinking in descending order ; habbit, business and reduce of stress, no reason, syndrome of stop drinking 10. Distribution of frequency of drinking in descending order ; daily, four or five times a week, irregularly, once a week, two or three times a week 11. Distribution of amount of drinking in descending order ; two bottles, one bottle, three bottles, half, bottle above four bottles 12. Distribution of Chief Complaint of Alcohol in descending order ; no appetite and anorexia, diarrhrea insomnia, fatigue, vomitting, tremor, drinking water, hallucination, abdominal pain, constipation 13. Distribution of total MAST score in descending order ; 26-48 score, 13-18 score, 19-25 score, 8-12 score, 0-7 score 14. In the treatment effects according to MAST score, these were complete stop drinking 18.0%, improved 53.0%, unchanged 29.0%. 15. Distribution of liver function test and treatment effects in descending order ; ALAT, ASAT, GGTP, Trigliceride, Alk-phosphatase and Total bilirubin The treatment effects in ear acupuncture were 70.5% effective ones ; stop drinking 17.6%, improved 52.9%. 17. These were headache, nausea, vomitting sense, weakness in revealing symtoms after treatment, but no severe side effect. 18. Distribution of the times of onset in the change of taste in descending order; 3-5 times, below 2 times and above 6 times.

• Journal of the Korean Data and Information Science Society
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• 제10권2호
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• pp.299-311
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• 1999

In this paper the single and product moments of order statistics of the doubly truncated Rayleigh distribution are studied. Some recurrence relations of order statistics are derived. Using order statistics, also characterization of the Rayleigh distribution are derived.

• Journal of applied mathematics & informatics
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• 제35권5_6호
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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.

• 산업경영시스템학회지
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• 제20권42호
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• pp.31-38
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• 1997

The main objective of this research is to develop a model to select the optimal input service level for a distribution center - multi branch inventory distribution system. With the continuous review policy, the distribution center places an order for specific order quantity to an outside supplier, and the order quantity is replenished after a certain lead time. Also, each branch places an order for particular order quantity to the distribution center to satisfy the customer demands, and receives the replenishment after a lead time. When an out of stock condition occurs during an order cycle, a backorder is placed to the upper level to fill the unfilled demands. With these situation, variable demand and variable lead time are used for better industrial practice. Further, actual lead times with a generic lead time distribution are used in developing the control model. Under the actual lead time model, the customer service measures actually attained for the distribution center and each branch are explained as the effective customer service measures. Thus, throughout the optimal control (using computer search procedures), we can select the optimal input service levels for the distribution center and each branch to attain the effective service level for each branch which is consistent with the goal level of service for each branch. At the same time, the entire distribution system keeps minimum inventories.

• 산업경영시스템학회지
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• 제20권42호
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• pp.21-30
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• 1997

This research fundamentally deals with an analysis of service level for a multi-level inventory distribution system which is consisted of a central distribution center and several branches being supplied stocks from the distribution center, Under continuous review policy, the distribution center places an order for planned order quantity to an outside supplier, and the order quantity is received after a certain lead time. Also, each branch places an order for particular quantity to its distribution center, and receives the order quantity after a lead time. In most practical distribution environment, demands and lead times are generally not fixed or constant, but variable. And these variabilities make the analysis more complicated. Thus, the main objective of this research is to suggest a method to compute the service level at each depot, that is, the distribution center and each branch with variable demands and variable lead times. Further, the model will give an idea to keep the proper level of safety stocks that can attain effective or expected service level for each depot.