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The Lomax distribution has had wide application in a variety of fields. It has been used in the analysis of income data, business failure data, and atmospheric data. In this article, we propose new approaches for the confidence intervals of the shape parameter of the Lomax distribution based on the maximum likelihood (ML) approach, bootstrap (BS) approach, Bayesian approach using Jeffreyss Prior (BJ) and Conjugate Prior (BC), and generalized probability weighted moment (GPWM). The performance of each method is assessed by simulation in terms of the coverage probabilities and average widths by the Monte Carlo simulation. An extensive simulation study indicates that the ML approach performs better than other approaches because it provides coverage probability close to the nominal confidence level, and the average widths are narrow. Moreover, the GPWM approach is regarded as a recommended method when the parameters α and β are high. We also illustrate our confidence intervals using a real world example in the area of meteorology.

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