Weighted Version of Generalized Inverse Weibull Distribution

Abstract

Weighted distributions are used in many fields, such as medicine, ecology, and reliability. A weighted version of the generalized inverse Weibull distribution, known as weighted generalized inverse Weibull distribution (WGIWD), is proposed. Basic properties including mode, moments, moment generating function, skewness, kurtosis, and Shannon’s entropy are studied. The usefulness of the new model was demonstrated by applying it to a real-life data set. The WGIWD fits better than its submodels, such as length biased generalized inverse Weibull (LGIW), generalized inverse Weibull (GIW), inverse Weibull (IW) and inverse exponential (IE) distributions.

Parameter Estimation of the Weighted Generalized Inverse Weibull Distribution

“…Weighted distributions were used frequently in research related to reliability, biomedicine, ecology and branching processes can be seen in Patil and Rao [3], Gupta and Kirmani [4], Gupta and Keating [5], Oluyede [6] and in references there in. There are many researchers for weighted distribution as Das and Roy [7] discussed the length-biased weighted generalized Rayleigh distribution with its properties, Sofi et al [8] studied the structural properties of length-biased Nakagami distribution. For more important results of weighted distribution see Oluyede and George [9], Ghitany and Al-Mutairi [10], Ahmed, Reshi and Mir [11], Sofi et al [12].…”