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Honam mathematical journal = 호남수학학술지 v.26 no.4, 2004년, pp.463 - 469   피인용횟수: 2

### RECURRENCE RELATIONS FOR QUOTIENT MOMENTS OF THE EXPONENTIAL DISTRIBUTION BY RECORD VALUES

LEE, MIN-YOUNG
• #### 초록

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the exponential distribution. Let $\{X_n,\;n{\geq}1\}$ be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function(pdf) f(x). Let $Y_n=max\{X_1,\;X_2,\;{\cdots},\;X_n\}$ for $n{\geq}1$ . We say $X_j$ is an upper record value of $\{X_n,\;n{\geq}1\}$ , if $Y_j>Y_{j-1}$ , j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, $n{\geq}1$ , where u(n)=min\{j{\mid}j>u(n-1),\;X_j>X_{u(n-1)},\;n{\geq}2\} and u(1) = 1. Suppose $X{\in}Exp(1)$ . Then $\Large{E\;\left.{\frac{X^r_{u(m)}}{X^{s+1}_{u(n)}}}\right)=\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n)}}}\right)}$ and $\Large{E\;\left.{\frac{X^{r+1}_{u(m)}}{X^s_{u(n)}}}\right)=\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m-1)}}{X^s_{u(n-1)}}}\right)}$ .

• #### 주제어

record value .   exponential distribution .   recurrence relation .   expectation.

• #### 참고문헌 (7)

1. Recurrence relations for single and product moments of record values from generalized pareto distribution , Balakrishnan, N.;Ahsanuallah, M. , Commun. Staist. Theor. Meth. / v.23,pp.2841-2852,
2. Relations for single and product moments of record values from exponential distribution , Balakrishnan, N.;Ahsanuallah, M. , J. Appl. Statist. Sci / v.,pp.,
3. Recurrence relations for moments of record values from generalized extreme value distribution , Balakrishnan, N.;Ahsanuallah, M.;Chan, P.S. , Commun. Staist.- Theor. Meth. / v.22,pp.1471-1482,
4. Relations for single and product moments of record values from Gumbel distribution , Balakrishnan, N.;Ahsanuallah, M.;Chan, P.S. , Staist.Probab. Lett. / v.15,pp.223-227,
5. The distribution and frequency of record values , Chandler, K.N. , J. R. Statist. Soc. B / v.14,pp.220-228,
6. Characterization of probability distributions , Galambos, J.;Katz, S. , / v.,pp.,
7. Record Statistics , Ahsanuallah, M. , / v.,pp.,
• #### 이 논문을 인용한 문헌 (2)

1. 2013. "" Journal of applied mathematics & informatics, 31(3): 327~336
2. 2014. "" Journal of applied mathematics & informatics, 32(1): 7~16

저자의 다른 논문

• #### Lee, Min-Young (26)

1. 1995 "An improved bonferroni-type inequality" Bulletin of the Korean Mathematical Society = 대한수학회보 32 (2): 329~336
2. 1996 "OPTIMAL BIVARIATE BONFERRONI-TYPE INQUALITIES VIA TAKING AVERAGE" Journal of the Korean Mathematical Society = 대한수학회지 33 (4): 793~799
3. 1997 "BOUNDS ON PROBABILITY FOR THE OCCURRENCE OF EXACTLY r, t OUT OF m, n EVENTS" Communications of the Korean Mathematical Society = 대한수학회논문집 12 (2): 393~401
4. 1999 "THE OPTIMAL BIVARIATE BONFERRONI-TYPE LOWER BOUNDS" Communications of the Korean Mathematical Society = 대한수학회논문집 14 (4): 789~795
5. 2001 "ON A CHARACTERIZATION OF THE EXPONENTIAL DISTRIBUTION BY CONDITIONAL EXPECTATIONS OF RECORD VALUES" Communications of the Korean Mathematical Society = 대한수학회논문집 16 (2): 287~290
6. 2002 "CHARACTERIZATIONS OF THE EXPONENTIAL DISTRIBUTION BY ORDER STATISTICS AND CONDITIONAL" Communications of the Korean Mathematical Society = 대한수학회논문집 17 (3): 535~540
7. 2003 "CHARACTERIZATIONS OF THE PARETO DISTRIBUTION BY CONDITIONAL EXPECTATIONS OF RECORD VALUES" Communications of the Korean Mathematical Society = 대한수학회논문집 18 (1): 127~131
8. 2003 "CHARACTERIZATIONS OF BETA DISTRIBUTION OF THE FIRST KIND BY CONDITIONAL EXPECTATIONS OF RECORD VALUES" Journal of applied mathematics & computing 13 (1): 441~446
9. 2003 "IMPROVED UPPER BOUNDS OF PROBABILITY" Communications of the Korean Mathematical Society = 대한수학회논문집 18 (4): 725~736
10. 2004 "RECURRENCE RELATIONS FOR QUOTIENT MOMENTS OF THE PARETO DISTRIBUTION BY RECORD VALUES" Journal of the Korean Society of Mathematical Education. 한국수학교육학회지. Series B, Pure and applied mathematics 11 (1): 97~102

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