Length Biased Gumbel Distribution And Its Application To Wind Speed Data.

Abstract

The concept of length biased distribution can be employed in development of proper models for life time data. Its method is adjusting the original probability density function from real data and the expectation of those data. This adjustment can bring about correct conclusions on the models. In this research, a new class of length biased approach was introduced to gumbel distribution which is called length baised gumbel distribution (LBGD). The theoretical properties of this distribution were derived and the model parameters were also estimated by Maximum Likelihood Estimation (MLE). This procedure is to adjust the original probability density function from real and ex-pected data which leads to good conclusion on the model. This distribution was later applied to wind speed data (extreme value data).

Keywords: Extreme Value Theory, Weighted Distribution, Length biased Gumbel Distribution, Alkaine Information Criterion, Wald Test