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NEW WEIGHTED PARETO DISTRIBUTION WITH APPLICATIONS TO MEDICAL AND ENGINEERING DATA
Keywords:
new weighted Pareto distribution, unimodal, upside-down bathtub failure rate function, heavy tailed distribution, maximum likelihood estimatorsDOI:
https://doi.org/10.17654/0972361725029Abstract
In statistical analyses, it is sometimes noted that the data under consideration may not accurately reflect the random behavior of the entire population, often due to the lower probability of certain subjects being included in the sample. This leads to biased estimations when drawing conclusions from such data sets. Recent years have seen the suggestion of length-biased distributions as a way to minimize this bias, thereby improving inferences. To address this issue, a new weighted Pareto (NWP) distribution is proposed. The Pareto distribution is highly applicable due to its simplicity, and the proposed weighting approach results in a novel distribution based on the Pareto model. The failure rate of the NWP distribution exhibits an inverted bathtub shape. A simulation study is conducted to assess the performance of the estimation methods under varying parameter values and sample sizes. Finally, a statistical analysis of real-world data sets demonstrates that the proposed model offers a superior fit compared to both the original length-biased model and other competing models.
Received: August 8, 2022
Revised: June 23, 2024
Accepted: February 8, 2025
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