Estimation of the Location and Scale Parameters of a Pareto Distribution by Linear Functions of Order Statistics

1973 ◽  
Vol 68 (341) ◽  
pp. 218-227 ◽  
Author(s):  
Gunnar Kulldorff ◽  
Kerstin Vännman
Keyword(s):  
Order Statistics ◽  
Pareto Distribution ◽  
Linear Functions ◽  
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.

scholarly journals Inference on Exponentiated Power Lindley Distribution Based on Order Statistics with Application

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Mansour Shrahili ◽  
Naif Alotaibi ◽  
Devendra Kumar ◽  
A. R. Shafay
Keyword(s):  
Order Statistics ◽  
Real Data ◽  
Linear Functions ◽  
Lindley Distribution ◽  
Scale Parameters ◽  
Power Lindley Distribution ◽  
Censored Sample ◽  
Best Linear Unbiased ◽  
Edgeworth Approximation ◽  
Mean Variance

Exponentiated power Lindley distribution is proposed as a generalization of some widely well-known distributions such as Lindley, power Lindley, and generalized Lindley distributions. In this paper, the exact explicit expressions for moments of order statistics from the exponentiated power Lindley distribution are derived. By using these relations, the best linear unbiased estimates of the location and scale parameters, based on type-II right-censored sample, are obtained. Next, the mean, variance, and coefficients of skewness and kurtosis of some certain linear functions of order statistics are calculated and then used to derive the approximate confidence interval for the location and scale parameters using the Edgeworth approximation. Finally, some numerical illustrations and two real data applications are presented.

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