Confidence Intervals and Tests for Two Exponential Scale Parameters Based On Order Statistics in Compressed Samples

Technometrics ◽  
1974 ◽  
Vol 16 (2) ◽  
pp. 251-254 ◽  
Author(s):  
Kenneth S. Kaminsky
Keyword(s):  
Order Statistics ◽  
Confidence Intervals ◽  
Scale Parameters

Stochastic comparison of parallel systems with Pareto components

2021 ◽  
pp. 1-13
Author(s):  
Sameen Naqvi ◽  
Weiyong Ding ◽  
Peng Zhao
Keyword(s):  
Order Statistics ◽  
Extreme Value Theory ◽  
Pareto Distribution ◽  
Parallel Systems ◽  
Value Theory ◽  
Extreme Value ◽  
Stochastic Comparison ◽  
Shape Parameters ◽  
Scale Parameters ◽  
Dispersive Ordering

Abstract Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686–687] from support $(0, \infty )$ to general supports $(a, \infty )$ , $a > 0$ . As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering.

Confidence intervals based on interpolated order statistics

1986 ◽  
Vol 4 (2) ◽  
pp. 75-79 ◽  
Author(s):  
Thomas P Hettmansperger ◽  
Simon J Sheather
Keyword(s):  
Order Statistics ◽  
Confidence Intervals
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