SINE-LOMAX DISTRIBUTION: PROPERTIES AND APPLICATIONS TO REAL DATA SETS

Abstract

In this study, a novel distribution called the two-parameter Sine Lomax distribution was introduced. The distribution was developed by combining the Sine generalized family of distributions with the Lomax distribution. Various statistical properties of this new distribution were investigated, including the survival function, hazard function, quantile function, rth moment, entropy, moment generating function, and order statistics. The probability density function (PDF) plot indicated that the distribution is skewed to the right. Additionally, the hazard plot of the Sine Lomax distribution showed both monotonic increase and monotonic decrease. To estimate the parameters of the newly proposed distribution, the maximum likelihood approach was employed. A simulation study was conducted to evaluate the consistency of the estimators. The simulation results indicated that the estimators are consistent, as the bias and mean square error decrease with increasing sample sizes. The performance of the Sine Lomax distribution was compared to other extensions of Lomax distributions and the baseline distribution which is the Lomax distribution using various evaluation criteria, including the Akaike Information Criterion (AIC), Consistent Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC), and Hannan-Quinn Information Criterion (HQIC). The proposed distribution demonstrated the lowest scores among the competing models, indicating its potential for accurately modeling real-world data sets. Based on the results, the proposed Sine Lomax distribution is recommended as a superior alternative to the competing models for modeling certain real-world data sets.