Open AccessA new inverse Weibull distribution: properties, classical and Bayesian estimation with applications
Author(s) -
Ahmed Z. Afify,
Ahmed Shawky,
Mazen Nassar
Publication year - 2021
Publication title -
maǧallaẗ al-kuwayt li-l-ʿulūm
Language(s) - English
Resource type - Journals
eISSN - 2307-4116
pISSN - 2307-4108
DOI - 10.48129/kjs.v48i3.9896
Subject(s) - weibull distribution , mathematics , rayleigh distribution , frequentist inference , inverse , logarithm , estimator , inverse distribution , exponential function , bayesian probability , inverse gamma distribution , inverse gaussian distribution , distribution (mathematics) , exponential distribution , statistics , bayesian inference , distribution fitting , inverse chi squared distribution , mathematical analysis , probability density function , heavy tailed distribution , geometry
This article proposes a new extension of the inverse Weibull distribution called, logarithmic transformed inverse Weibull distribution which can provide better fits than some of its well-known extensions. The proposed distribution contains inverse Weibull, inverse Rayleigh, inverse exponential, logarithmic transformed inverse Rayleigh and logarithmic transformed inverse exponential distributions as special sub-models. Our main focus is to derive some of its mathematical properties along with the estimation of its unknown parameters using frequentist and Bayesian estimation methods. We compare the performances of the proposed estimators using extensive numerical simulations for both small and large samples. The importance and potentiality of this distribution is analyzed via two real data sets.