Approximate MLEs for the location and scale parameters of the extreme value distribution with censoring

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

The Scientific World JOURNAL ◽

10.1155/2013/281624 ◽

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.

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Comparative Study of Blu and ML Estimators of Location and Scale Parameters of an Extreme Value Distribution for Small Samples and Type I Censorship

Communications in Statistics - Simulation and Computation ◽

10.1080/03610918908812779 ◽

1989 ◽

Vol 18 (2) ◽

pp. 601-611 ◽

Cited By ~ 1

Author(s):

Mohamed M. Bugaighis

Keyword(s):

Comparative Study ◽

Extreme Value Distribution ◽

Extreme Value ◽

Value Distribution ◽

Small Samples ◽

Type I ◽

Scale Parameters

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A study of trends for Mexico City ozone extremes: 2001-2014

Atmósfera ◽

10.20937/atm.2016.29.02.01 ◽

2016 ◽

Vol 29 (2) ◽

pp. 107 ◽

Cited By ~ 9

Author(s):

Sara Rodríguez ◽

Gabriel Huerta ◽

Hortensia Reyes

Keyword(s):

Mexico City ◽

Bayesian Methods ◽

Time Trends ◽

Extreme Value Distribution ◽

Location Parameter ◽

Extreme Value ◽

Value Distribution ◽

Generalized Extreme Value Distribution ◽

Scale Parameters ◽

Ozone Levels

We analyze trends of high values of tropospheric ozone over Mexico City based on data corresponding to the years 2001-2014. The data consists of monthly maxima ozone concentrations based on 29 monitoring stations. Due to the large presence of missing data, we consider the monthly maxima based on five well identified geographical zones. We assess time trends based on a statistical model that assumes that these observations follow an extreme value distribution, where the location parameter changes in time accordingly to a regression model. In addition, we use Bayesian methods to estimate simultaneously a zonal and an overall time-trend parameter along with the shape and scale parameters of the Generalized Extreme Value distribution. We compare our results to a model that is based on a normal distribution. Our analyses show some evidence of decaying ozone levels for the monthly maxima during the period of study.

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