A study at the University of Karbala discusses  A New Statistical Distribution Using the DUS Transformation with a Practical Application

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A study at the University of Karbala discusses  A New Statistical Distribution Using the DUS Transformation with a Practical Application

A New Statistical Distribution Using the DUS Transformation with a Practical Application

A thesis submitted to

the Council of the College of Administration and Economics /

University of Karbala,

as part of the requirements for the degree of Master in Statistics

Submitted by:

Zahraa Ahmed Hashem Abd

Supervised By:

Asst. Prof. Dr. Enas Abdul-Hafidh Mohammed Asst. Prof. Zainab Hassan Aboud

The DUS-X Shanker distribution is a newly developed probabilistic model obtained by combining the DUS Transformation with the X-Shanker distribution.
It aims to provide greater statistical flexibility in modeling complex real-world data, particularly lifetime and reliability data.

The study involved deriving the fundamental functions of the new distribution, including the Probability Density Function (PDF), the Cumulative Distribution Function (CDF), the Survival Function, and the Hazard Function, in addition to analyzing its statistical properties such as the mean, variance, and moments.

Three estimation methods were employed to estimate the distribution parameter:

  • Maximum Likelihood Estimation (MLE)
  • Ordinary Least Squares (WLS)
  • Modified Maximum Likelihood Estimation (MMLE)

Their efficiencies were evaluated through simulation experiments using random data generated with different sample sizes (50, 75, 100, 150) in MATLAB, with the Mean Squared Error (MSE) adopted as the main comparison criterion.

The simulation results revealed that the MLE method outperformed the others in terms of accuracy and stability, especially for larger sample sizes.
In contrast, the MMLE method showed noticeable bias in the estimates, while the WLS method was the least efficient.

For the practical application, the proposed distribution was applied to real data of kidney failure patients.
The results demonstrated that the DUS-X Shanker distribution provided a better fit than the original X-Shanker distribution, based on the Kolmogorov–Smirnov (K-S) test and model selection criteria (AIC, BIC, CAIC).

These findings highlight the importance of the DUS-X Shanker distribution as a flexible and effective statistical tool for modeling medical survival data, as well as its role in improving prediction accuracy and supporting medical decision-making regarding disease progression.