Inverse unit compound Rayleigh distribution: statistical properties with applications in different fields

The present article presents a novel two-parameter distribution called inverse unit compound Rayleigh distribution (IUCRD), which has the support (1,). It is propounded via the inverse transformation of the unit compound Rayleigh distribution (UCRD). Different properties of the IUCRD, namely, the quantile function, the mode, stochastic ordering, moments, and heavy-tailedness, among others, are explored. We notice that the distribution PDF is either unimodal or nonincreasing. It can also be left-skewed or right-skewed, depending on the values of the parameters of the IUCRD. The graph of the hazard rate function of the IUCRD is the upside-down bathtub shape or nondecreasing. Heavy-tailedness is also among the properties of the IUCRD determined in this work. We provide evidence of the relationship between the IUCRD and exponential distribution via the derivation of distributions of certain functions of one variable. Sixteen different estimation methods are compared employing the Monte Carlo simulation procedure. Numerical simulation evidence attests to the KE method being the best estimation methodology for the parameters of the IUCRD. Interestingly, according to the simulation results, the ML procedure assumes the second position. In demonstrating the usefulness of the IUCRD, we use the ML technique to fit the distribution to five real-world datasets and compare its fits with the fits of seven existing distributions to the data by employing goodness of fit statistics. For each of the data, the minimum value of each of the statistics corresponds to the IUCRD. This result makes it clear that in many data analysis circumstances, the IUCRD can be preferable to several continuous distributions, especially the UCRD and the inverse unit exponential, inverse Weibull, inverse Rayleigh, inverse Chen, inverse exponential, and inverse exponential distributions.