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A New Lomax Exponentiated Exponential Distribution: Statistical Properties, Parameter Estimation and Applications to Real Data

Yusuf Saadatu Aliyu1, Umar Usman2, Aminu Bello Zoramawa3, AbdulAziz Mohammed, Ndatsu4

Abstract

The development of flexible probability distributions has continued to receive considerable attention in statistical modelling because classical probability models frequently fail to accommodate skewed observations, heavy tails and varying hazard rate structures encountered in practice. Although the Lomax distribution has been extensively applied in reliability engineering, actuarial science, finance and survival analysis, its limited flexibility restricts its applicability to many real-life datasets. This study introduces a new three-parameter continuous probability model called the New Lomax Exponentiated Exponential Distribution by combining the New Lomax generator with the Exponential distribution under the T–X family framework. Mathematical expressions for the cumulative distribution function, probability density function, survival function, hazard rate function, reversed hazard rate function, quantile function, moment generating function and characteristic function were derived. Unknown model parameters were estimated using the Maximum Likelihood Estimation method. The applicability of the proposed model was evaluated using two real lifetime datasets and compared with existing probability distributions including the Lomax, Burr III, Log-logistic and Generalized Extreme Value distributions. Model comparison was performed using the Akaike Information Criterion , Bayesian Information Criterion , Consistent Akaike Information Criterion , Hannan–Quinn Information Criterion and the Kolmogorov–Smirnov goodness-of-fit statistic. The empirical findings indicate that the proposed distribution consistently produced lower information criteria values than competing models, demonstrating superior flexibility in modelling skewed and heavy-tailed observations. The results establish the proposed distribution as an effective alternative for modelling lifetime and reliability data and contribute to the growing family of generalized probability distributions. IJASMT E- ISSN 2489-009X ,

Keywords

New Lomax DistributionExponentiated Exponential DistributionHeavy-tailed DistributionMaximum Likelihood EstimationReliability AnalysisSurvival AnalysisT–X Family.

References

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