A New Power Topp-Leone distribution with applications to engineering and industry data

Area of Science:

• Statistics
• Probability Distributions

Background:

• The development of new statistical distributions is crucial for improving data modeling and analysis.
• Existing models may not adequately capture the complexities of all real-world phenomena.

Purpose of the Study:

• To introduce and mathematically define a novel probability distribution, the New Power Topp-Leone Generated (NPTL-G) distribution.
• To explore the mathematical properties and potential applications of the NPTL-G distribution.

Main Methods:

• Derivation of key mathematical functions including Rényi entropy, qf, series development, and moment weighted probabilities.
• Estimation of model parameters using the maximum likelihood technique.
• Validation of the proposed model using two real-world datasets.

Main Results:

• The NPTL-G distribution was mathematically formulated with detailed derivations of its properties.
• The maximum likelihood estimation method was successfully applied to estimate model parameters.
• Empirical analysis showed the NPTL-G distribution outperforms three competing models.

Conclusions:

• The NPTL-G distribution is a promising new statistical model with demonstrated advantages.
• The model's flexibility and performance suggest broad applicability in various fields requiring statistical modeling.