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Estimation of any probability distribution parameters is vital because imprecise and biased estimates can be misleading. In this study, we investigate a flexible power function distribution and introduced new two methods such as, probability weighted moments, and generalized probability weighted methods for its parameters. We compare their results with L-moments, trimmed L-moments by a simulation study and a real data example based on performance measures such as, mean square error and total deviation. We concluded that all the methods perform well in the case of large sample size (n>30), however, the generalized probability weighted moment method performs better for small sample size.

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