Truncated Cauchy power Zeghdoudi distribution with applications in different sciences

Many new, improved, adaptable, and reliable probability distributions have recently been created from existing ones to promote their use in various domains. This study combines the Zeghdoudi distribution (ZD) and the truncated Cauchy power (TCP)-G family to create a novel two-parameter lifespan distribution called TCP-ZD. The novel distribution is distinguished from the ZD by its extremely flexible behavior. The probability density and hazard rate functions exhibit increasing, decreasing, J, and reverse J shapes, which provide early indications of the potential for adaptability of the related model. Its mathematical characteristics are thoroughly covered, with formulas for the moments, quantiles, moment generating function, stochastic ordering, incomplete moments, inequality measures, extropy and weighted extropy measures. The TCP-ZD parameters are estimated using fifteen different approaches, and an in-depth simulation investigation is conducted to examine each method’s effectiveness. To identify the best estimation strategy, several precision measures are displayed, including bias, mean squared errors, mean relative errors, average absolute difference, maximum absolute difference, and partial and overall ranks of these estimates. The simulation results indicate that the maximum likelihood and maximum product spacing methods were most effective in estimating the TCP-ZD parameters. With low accuracy measure values, TCP-ZD showed stability. With higher sample sizes, all approaches demonstrated increased accuracy in estimating. We examine eight real-world datasets to demonstrate the TCP-ZD’s usefulness in practice. Using several goodness-of-fit metrics, we show that the TCP-ZD offers a better match to the data sets.