Template:Gumbel distribution introduction

Introduction

The Gumbel distribution is also referred to as the Smallest Extreme Value (SEV) distribution or the Smallest Extreme Value (Type I) distribution. The Gumbel distribution's [math]\displaystyle{ pdf }[/math] is skewed to the left, unlike the Weibull distribution's [math]\displaystyle{ pdf }[/math] , which is skewed to the right. The Gumbel distribution is appropriate for modeling strength, which is sometimes skewed to the left (few weak units in the lower tail, most units in the upper tail of the strength population). The Gumbel distribution could also be appropriate for modeling the life of products that experience very quick wear-out after reaching a certain age. The distribution of logarithms of times can often be modeled with the Gumbel distribution (in addition to the more common lognormal distribution) [27].