The Exponentiated Chen Inverse Rayleigh Distribution: Its Properties and Parameter Estimation.

Abstract:

This study proposed an Exponential Chen Inverse Rayleigh (ECIR) distribution to the tackle the difficulties of modeling failure rates that exhibit both monotonic and non-monotonic behavior, as well as appropriately capturing the bathtub curve in reliability engineering. The properties of the ECIR distribution like the survival function, hazard function, cumulative Hazard function, moments and ordered statistics were derived. The simulation result for median, skewness, and kurtosis of ECIRD (β,λ,δ,φ) with different parameter values of β,λ, δ and φ result indicated that the distributions are right-skew, with peakness and tail behavior similar to that of a normal distribution, albeit with some variations. Findings from the application of ECIRD to the survival times (in days) for 72 guinea pigs infected with virulent tubercle bacilli, revealed that ECIR model emerge as the most preferred among the competing models. The ECIR model exhibits the best overall performance, with the lowest values for -2LL which confirms that it provides the most parsimonious fit to the data. The proposed ECIR model also exhibited standard errors that suggest variability in the estimates.