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Estimation methods based on ranked set sampling for the power logarithmic distribution.

Najwan Alsadat¹, Amal S Hassan², Mohammed Elgarhy^3,4

¹Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, 11587, Riyadh, Saudi Arabia.

Scientific Reports

|July 31, 2024

Summary

This summary is machine-generated.

Ranked set sampling (RSS) improves statistical parameter estimation accuracy for the bounded power logarithmic distribution (PLD). Maximum product spacing estimates using RSS are more efficient than simple random sampling (SRS) methods.

Keywords:

Average squared absolute error Minimum spacing Linex distance Minimum spacing square log distance Power logarithmic distribution Ranked set sampling

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Area of Science:

Statistics
Statistical Modeling

Background:

Accurate statistical parameter estimation is crucial for data analysis.
Ranked set sampling (RSS) offers an efficient data collection method, especially when direct quantification is challenging.
The bounded power logarithmic distribution (PLD) is a recent distribution suitable for bounded real-world data.

Purpose of the Study:

To estimate the three parameters of the bounded power logarithmic distribution (PLD) using ranked set sampling (RSS).
To compare the efficiency of various estimation methods under RSS with their simple random sampling (SRS) counterparts.

Main Methods:

Estimation of PLD parameters using RSS.
Investigation of multiple conventional estimators: Maximum Likelihood, Minimum Spacing variants, Anderson-Darling, Least Squares, Cramer-von-Mises, and Maximum Product of Spacings.
Comparative analysis of RSS estimates against SRS estimates through simulations.
Validation using a real-world data example.

Main Results:

The Maximum Product Spacing (MPS) estimation method demonstrated superior performance for both SRS and RSS datasets.
Estimates derived using RSS were consistently more efficient than those obtained through SRS.
Ranked set sampling (RSS) significantly enhances the accuracy and efficiency of parameter estimation for the PLD.

Conclusions:

Ranked set sampling (RSS) is a valuable technique for improving the estimation of parameters for the bounded power logarithmic distribution (PLD).
The Maximum Product Spacing (MPS) method, when combined with RSS, provides the most efficient estimates.
The findings highlight the practical utility of RSS estimators in real-world applications.