6 Estimation of scale parameter based on a fixed set of order statistics

1998 ◽  
pp. 159-181
Author(s):  
Sanat K. Sarkar ◽  
Wenjin Wang
Keyword(s):  
Order Statistics ◽  
Scale Parameter ◽  
Fixed Set

ON PARALLEL SYSTEMS WITH HETEROGENEOUS GAMMA COMPONENTS

2011 ◽  
Vol 25 (3) ◽  
pp. 369-391 ◽  
Author(s):  
Peng Zhao
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Shape Parameter ◽  
Scale Parameter ◽  
Random Variables ◽  
Parallel Systems ◽  
Likelihood Ratio Order ◽  
Maximum Order ◽  
Hazard Rate Order

In this article, we study ordering properties of lifetimes of parallel systems with two independent heterogeneous gamma components in terms of the likelihood ratio order and the hazard rate order. LetX1andX2be two independent gamma random variables withXihaving shape parameterr>0 and scale parameter λi,i=1, 2, and letX*1andX*2be another set of independent gamma random variables withX*ihaving shape parameterrand scale parameter λ*i,i=1, 2. Denote byX2:2andX*2:2the corresponding maximum order statistics, respectively. It is proved that, among others, if (λ1, λ2) weakly majorize (λ*1, λ*2), thenX2:2is stochastically greater thanX*2:2in the sense of likelihood ratio order. We also establish, among others, that if 0<r≤1 and (λ1, λ2) isp-larger than (λ*1, λ*2), thenX2:2is stochastically greater thanX*2:2in the sense of hazard rate order. The results derived here strengthen and generalize some of the results known in the literature.

scholarly journals Scale Parameter Estimation from the Order Statistics of Unequal Gamma Components

1966 ◽  
Vol 37 (1) ◽  
pp. 152-176 ◽  
Author(s):  
M. B. Wilk ◽  
R. Gnanadesikan ◽  
Elizabeth Lauh
Keyword(s):  
Parameter Estimation ◽  
Order Statistics ◽  
Scale Parameter

scholarly journals On the BLUE of the scale parameter of the generalized Pareto distribution

2000 ◽  
Vol 31 (3) ◽  
pp. 165-174
Author(s):  
S. W. Cheng ◽  
C. H. Chou
Keyword(s):  
Order Statistics ◽  
Pareto Distribution ◽  
Scale Parameter ◽  
Generalized Pareto Distribution ◽  
Generalized Pareto ◽  
Sigma 1 ◽  
Censored Sample ◽  
Unbiased Estimates ◽  
Best Linear Unbiased ◽  
Type Ii Censored Sample

In this article, we will study the linear estimation of the scale parameter of the generalized Pareto distribution (GPD) which has the probability density function (p.d.f.)$$ f(x)=\left\{\begin{array}{ll} \sigma^{-1}(1-rx/\sigma)^{1/r-1},~~& r\not=0 \\ \sigma^{-1}\exp(-x/\sigma),&r=0. \end{array}\right.$$We first derive the expected value, variances and covariances of the order statistics from the GPD. Then proceed to find the best linear unbiased estimates of the scale parameter $\sigma$ based on a few order statistics selected from a complete sample or a type-II censored sample. Results of some chosen cases were tabulated.

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