Probability Paper and Plotting Position of Extreme Value Distribution for Distribution Selection and Parameter Estimation
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Extreme Value distribution(EVD), Plotting Position(PP), Probability Paper Plot (PPP), Mean squared error(MSE)
Abstract
The problem of estimation for tail index in extreme value distributions is very important in many applications. Statistical methods could be used to select the distribution based on the available data, where the initially specified distributions or family of distributions usually depend on unknown parameters, and these parameters need to be estimated. This paper shows how probability papers plots (PPP) can be used to select the most appropriate distribution among the three types of maximum extreme value distribution (Gumbel, Weibull, and Fréchet). Another objective is to use the PPP for parameter estimation using the regression method. The last objective is to compare between PPP, MLE, and PWM methods to estimate the parameters of the selected distribution using two criteria: the mean square error and correlation coefficient. Results of using the daily maximum of temperature in weather data show that the Weibull distribution is the best distribution for each period of this data. Another result finding is that the PPP provides a more efficient estimate for the shape parameter of the Weibull distribution than the MLE and PWM methods dependent on mean square error.
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