This paper introduces a novel three-parameter skew-log-logistic distribution. The research involves the development of a new random variable based on Azzalini and Capitanio’s (2013) proposition. Additionally, various statistical properties of this distribution are explored. The paper presents a maximum likelihood method for estimating the distribution’s parameters. The density function exhibits unimodality with heavy right tails, while the hazard function exhibits rapid increase, unimodality, and slow decrease, resulting in a right-skewed curve. Furthermore, four real datasets are utilized to assess the applicability of this new distribution. The AIC and BIC criteria are employed to assess the goodness of fit, revealing that the new distribution offers greater flexibility compared to the baseline distribution.

Log-Logistic, skew, marriage, menarche, age-specific fertility rate.

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