Determining the wind load on structures is greatly influenced by the basic wind speed. A statistical analysis of past wind speed data collected through instruments is needed to determine its value. The Gumbel distribution is commonly used to model extreme wind speeds, which is determined by two parameters (α, β). Various techniques can be used to calculate both factors, which can have a significant impact on how well the distribution fits. The current study seeks to assess how sample size affects the goodness of fit provided by five methods: LS, BLUE, MOM, PWM, and ML. Moreover, determine which techniques provide superior results for datasets of varying sizes. The techniques are assessed using randomly created data and compared based on bias, mean squared error, and joint deficiency criteria. To achieve this goal, the Monte Carlo Technique is utilized, with sample sizes ranging from 10 to 30 data and 140–300 data being considered. Afterwards, the techniques are used on data collected from two weather stations in Cuba and the findings are compared to the speeds found in earlier research. The findings indicate that the size of the sample is not the sole factor affecting the methods’ performance on a particular data set.