Approximating the three parameters of Gumbel model through Lindley Bayes
Jyoti Pandey, Uma Srivastava · International Journal of Statistics and Applied Mathematics · 2025
The three-parameter Gumbel distribution has become very useful in recent years because it can be applied in many areas such as hydrology, climate studies, weather analysis, environmental research, and finance. The distribution is characterized by three parameters shape (α), scale (β), and location (γ) which together control the skewness, spread, and central tendency of the data. Accurate estimation of these parameters plays a key role in improving statistical modelling and inference. In this study, we use a Bayesian estimation method for finding the parameters of the three-parameter Gumbel distribution. The Bayesian approach is useful because it combines prior information about the parameters with the data, which helps in getting better estimates, especially when the sample size is small. The main difficulty in Bayesian methods is that the required calculations are often very complex. To deal with this problem, we apply Lindley’s approximation, which is a simple and efficient way to get approximate solutions. Using this method, we obtain the Approximate Bayes Estimators (ABEs) of the parameters α, β, and γ under the Squared Error Loss Function (SELF). The results show that ABS performs better in terms of mean squared error, especially for smaller sample sizes.