Transmuted unit new XLindley distribution: statistical properties, parameter estimation, and applications to bounded data

Abstract This paper proposes the transmuted unit new XLindley distribution (TUNXLD), a novel two-parameter probability model on the unit interval $(0,1)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:math> , obtained by applying the transmutation method to the unit new XLindley distribution. The transmutation parameter extends the base model to accommodate diverse density shapes, skewness levels, tail characteristics, and hazard rate profiles. Closed-form expressions are derived for the probability density function, cumulative distribution function, moments, quantile function, reliability measures, and Tsallis, Rényi, Havrda–Charvát, and Arimoto entropies. Parameter estimation is considered from the point of view of maximum likelihood and minimum-distance methods, and their consistency is checked in a Monte Carlo simulation. Applied to two unit-interval datasets: a socio-economic cable-penetration dataset and a genomic gene-expression dataset. Information criteria and goodness-of-fit tests show that TUNXLD is more adaptable and more useful than many competing distributions for modelling limited data in the fields of dependability, survivability, and data science.