Statistical Analysis of the Inverse Power Zeghdoudi Model: Estimation, Simulation and Modeling to Engineering and Environmental Data

Abstract

Abstract In this research, we investigate a brand-new two-parameter distribution as an extension of the
power Zeghdoudi distribution (PZD). Using the inverse transformation technique on the PZD, the
produced distribution is called the inverted PZD (IPZD). Its usefulness in producing symmetric and
asymmetric probability density functions makes it the perfect choice for lifetime phenomenon mod-
eling. It is also appropriate for a range of real data since the relevant hazard rate function has one of
the following shapes: increasing, decreasing, reverse j-shape or upside-down shape. Mode, quantiles,
moments, geometric mean, inverse moments, incomplete moments, distribution of order statistics,
Lorenz, Bonferroni, and Zenga curves are a few of the significant characteristics and aspects explored
in our study along with some graphical representations. Twelve effective estimating techniques are
used to determine the distribution parameters of the IPZD. These include the Kolmogorov, least
squares (LS), a maximum product of spacing, Anderson-Darling (AD), maximum likelihood, mini-
mum absolute spacing distance, right-tail AD, minimum absolute spacing-log distance, weighted LS,
left-tailed AD, Cram ́er-von Mises, AD left-tail second-order. A Monte Carlo simulation is used to
examine the effectiveness of the obtained estimates. The visual representation and numerical results
show that the maximum likelihood estimation strategy regularly beats the other methods in terms of
accuracy when estimating the relevant parameters. The usefulness of the recommended distribution
for modelling data is illustrated and displayed visually using two real data sets and comparisons with
other distributions.