• Journal of applied mathematics & informatics
• /
• 제5권1호
• /
• pp.41-50
• /
• 1998

There are various notions of partial ordering between life-times of systems; stochastic ordering failure rate ordering and likeli-hood ration ordering. In this paper we show that for series systems with non i.i.d. exponential lifetimes of components standby redundancy at component level is better than that at system level in failure rate or-dering and likelihood ratio ordering. We also demonstrate that for 2-component parallel systems with i.i.d. exponential lifetimes of com-ponents standby system redundancy is better than standby component redundancy in failure rate ordering and likelihood ratio ordering.

• Communications for Statistical Applications and Methods
• /
• 제18권4호
• /
• pp.485-493
• /
• 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
• /
• 제14권2호
• /
• pp.413-428
• /
• 2003

If a restriction is imposed only to a (proper) subset of parameters of interest, we call it a local restriction. Statistical inference under a local restriction in multinomial setting is studied. The maximum likelihood estimation under a local restriction and likelihood ratio tests for and against a local restriction are discussed. A real data is analyzed for illustrative purpose.

• Journal of the Korean Data and Information Science Society
• /
• 제15권1호
• /
• pp.201-210
• /
• 2004

The peakedness ordering is closely related to dispersive ordering. In this paper we consider the statistical inference concerning peakedness ordering between two arbitrary symmetric distributions. Nonparametric maximum likelihood estimates of two distribution functions under symmetry and peakedness ordering are given. The likelihood ratio test for equality of two symmetric discrete distributions in the sense of peakedness ordering is studied.

• Communications for Statistical Applications and Methods
• /
• 제16권6호
• /
• pp.1023-1029
• /
• 2009

Oh (2009) has proposed a likelihood ratio test for comparing two agreements for dependent observations based on the concept of marginal homogeneity and marginal stochastic ordering. In this paper we consider the comparison of more than two agreement measures. Simple ordering and simple tree ordering among agreement measures are investigated. Some test procedures, including likelihood ratio test, are discussed.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2003년도 춘계 학술발표회 논문집
• /
• pp.109-114
• /
• 2003

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter, which is peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose nonparametric maximum likelihood estimator of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• Journal of the Korean Statistical Society
• /
• 제33권3호
• /
• pp.303-312
• /
• 2004

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter. This is the peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose non parametric maximum likelihood estimators of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• 한국경영과학회:학술대회논문집
• /
• 한국경영과학회 1987년도 추계학술발표회 발표논문초록집; 중소기업협동조합중앙회, 서울; 31 Oct. 1987
• /
• pp.35-35
• /
• 1987

Consider a job shop that is modelled as an open queueing network of the Jackson(l957) type. All work stations in the shop have the same number of parallel servers. Two problems are studied : the loading of stations and the assignment of servers, which are represented by loading and assingment vectors, respectively. Ma jorization and arrangement orderings are established to order, respectively, the loading and the assignment vectors. It is shown that reducing the loading vector under ma jorizat ion or increasing the assignment vector under arrangement ordering will reduce the congestion in the shop in terms of reducing the total number of jobs(in the sense of likelihood ratio ordering), the maximum queue length(in the sense of stochastic ordering), and the queue-length vector( in the sense of stochastic majorization). The results can be used to supprot production planning in certain job shops, and to aid the desing of storage capacity. (OPEN QUEUEING NETWORK; WJORIZATION; ARRANGEMENT ORDERINC; LIKELIHOOD RATIO ORDERINC; STOCHASTIC ORDERING)

• Journal of the Korean Statistical Society
• /
• 제27권2호
• /
• pp.205-220
• /
• 1998

Dependence concepts for ordered two-way contingency tables have been of considerable interest. We consider a dependence concept which is less restrictive than likelihood ratio dependence and more restrictive than regression dependence. Maximum likelihood estimation of cell probability under this dependence restriction is studied. The likelihood ratio statistics for and against this dependence are proposed and their large sample distributions are derived. A real data is analyzed to illustrate the estimation and testing procedures.

• Journal of the Korean Statistical Society
• /
• 제23권2호
• /
• pp.349-365
• /
• 1994

We develop in this paper the likelihood ratio test (LRT) for testing $H_1 : F_1 \preceq F_2$ against $H_2 - H_1$ where $H_2$ imposes no restriction on $F_1$ and $F_2$ and '$\preceq$' means failure rate ordering. Both one and two-sample problems will be considered. In the one-sample case, one of the two distributions is known, while we assume in the other case both are unknown. We derive the asymptotic null distribution of the LRT statistic which will be of chi-bar-square type. The main issue here is to determine the least favorable distribution which is stochastically largest within the class of null distributions.