Abstract:
Rank transmutation maps have emerged as one of the adopted methods for
proposing new probability distributions. This study used the quartic rank transmutation
to introduce three new probability distributions: the Quartic Transmuted
Exponential Distribution, Quartic Transmuted Lindley Distribution, and
Quartic Transmuted Rayleigh Distribution. The construction of these distributions
involves meticulously examining mathematical concepts, encompassing
probability density functions, survival functions, moments, entropies, and order
statistics. Visual aids, including cumulative distribution functions, probability
density functions, and hazard rate functions, enhance the comprehension
of distribution characteristics. A comprehensive simulation study underscores
a consistent trend: a reduction in bias for maximum likelihood estimation and
refinement in standard errors with increasing sample size. The practical applicability
of these newly proposed distributions was demonstrated using real-world
datasets. The quartic transmuted exponential distribution was effectively employed
to model the lifetime of 50 devices, referencing data from Aarset’s study
in 1987. Similarly, the quartic transmuted Lindley distribution was adeptly applied
to remission times (measured in months) of 128 bladder cancer patients.
Finally, the quartic transmuted Rayleigh distribution was successfully utilized
to analyze a dataset comprising 72 instances of exceedance from the Wheaton
River flood data near Carcoss in Yukon Territory, Canada. Evaluation criteria
such as log-likelihood, AIC, AICc, and BIC affirm the superior flexibility
and performance of the proposed distributions. This research significantly contributes
to distribution theory, offering innovative methods to enhance distribution
adaptability in diverse applications.
