scholarly journals Weighted Moments Estimators of the Parameters for the Extreme Value Distribution Based on the Multiply Type II Censored Sample

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Jong-Wuu Wu ◽  
Sheau-Chiann Chen ◽  
Wen-Chuan Lee ◽  
Heng-Yi Lai
Keyword(s):  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Estimation Methods ◽  
Type Ii ◽  
Scale Parameters ◽  
Censored Sample ◽  
Best Linear Unbiased ◽  
Moments Estimators ◽  
Type Ii Censored Sample

We propose the weighted moments estimators (WMEs) of the location and scale parameters for the extreme value distribution based on the multiply type II censored sample. Simulated mean squared errors (MSEs) of best linear unbiased estimator (BLUE) and exact MSEs of WMEs are compared to study the behavior of different estimation methods. The results show the best estimator among the WMEs and BLUE under different combinations of censoring schemes.

Convergence rates for the ultimate and pentultimate approximations in extreme-value theory

1982 ◽  
Vol 14 (04) ◽  
pp. 833-854 ◽  
Author(s):  
Jonathan P. Cohen
Keyword(s):  
Extreme Value Theory ◽  
Convergence Rates ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Type I ◽  
Type Ii

Let F be a distribution in the domain of attraction of the type I extreme-value distribution Λ(x). In this paper we derive uniform rates of convergence of Fn to Λfor a large class of distributions F. We also generalise the penultimate approximation of Fisher and Tippett (1928) and show that for many F a type II or type III extreme-value distribution gives a better approximation than the limiting type I distribution.

Convergence rates for the ultimate and pentultimate approximations in extreme-value theory

1982 ◽  
Vol 14 (4) ◽  
pp. 833-854 ◽  
Author(s):  
Jonathan P. Cohen
Keyword(s):  
Extreme Value Theory ◽  
Convergence Rates ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Type I ◽  
Type Ii

Let F be a distribution in the domain of attraction of the type I extreme-value distribution Λ(x). In this paper we derive uniform rates of convergence of Fn to Λfor a large class of distributions F. We also generalise the penultimate approximation of Fisher and Tippett (1928) and show that for many F a type II or type III extreme-value distribution gives a better approximation than the limiting type I distribution.

scholarly journals Interval Estimation for Extreme Value Parameter with Censored Data

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Eun-Joo Lee ◽  
Dane Walker ◽  
David Elliott ◽  
Katlyn Mathy ◽  
Seung-Hwan Lee
Keyword(s):  
Weibull Distribution ◽  
Censored Data ◽  
Interval Estimation ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Finite Sample ◽  
Real World Data ◽  
Scale Parameters ◽  
Statistical Inferences

The Weibull distribution is widely used in the parametric analysis of lifetime data. In place of the Weibull distribution, it is often more convenient to work with the equivalent extreme value distribution, which is the logarithm of the Weibull distribution. The main advantage in working with the extreme value distribution is that unlike the Weibull distribution, the extreme value distribution has location and scale parameters. This paper is devoted to a discussion of statistical inferences for the extreme value distribution with censored data. Numerical simulations are performed to examine the finite sample behaviors of the estimators of the parameters. These procedures are then applied to real-world data.

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