A Flexible Heavy-Tailed Distribution via the Modified Kies Family: Theory and Applications

This paper introduces a new heavy-tailed distribution as an alternative to the classical Inverse Lomax distribution, constructed through the Modified Kies generator. The proposed Modified Kies Inverse Lomax distribution (MKILD) is designed to model real lifetime data characterised by skewness, high kurtosis, and the presence of outlying observations. Its density function exhibits considerable flexibility, accommodating decreasing, nearly symmetric, and left- or right-skewed unimodal shapes, while its hazard rate captures both increasing and decreasing patterns. Several statistical properties are derived, including order statistics, quantile function, moments, probability weighted moments, skewness, and kurtosis. Parameter estimation is carried out using six methods: maximum likelihood, maximum product of spacing, Anderson-Darling, Cramér-von Mises, least squares, and weighted least squares. Simulation studies confirm that biases and mean squared errors diminish consistently with increasing sample size, with maximum likelihood proving the most efficient across most settings. Three real-life applications to lifetime datasets establish that the MKILD provides a competitive fit compared to the classical ILD and several of its generalisations, namely the Power ILD, Marshall-Olkin ILD, Exponentiated Generalised ILD, and Odd Fréchet ILD.