Inverted Weibull Regression Models and Their Applications

Abstract

In this paper, we propose the classical and Bayesian regression models for use in conjunction with the inverted Weibull (IW) distribution; there are the inverted Weibull Regression model (IW-Reg) and inverted Weibull Bayesian regression model (IW-BReg). In the proposed models, we suggest the logarithm and identity link functions, while in the Bayesian approach, we use a gamma prior and two loss functions, namely zero-one and modified general entropy (MGE) loss functions. To deal with the outliers in the proposed models, we apply Huber and Tukey’s bisquare (biweight) functions. In addition, we use the iteratively reweighted least squares (IRLS) algorithm to estimate Bayesian regression coefficients. Further, we compare IW-Reg and IW-BReg using some performance criteria, such as Akaike’s information criterion (AIC), deviance (D), and mean squared error (MSE). Finally, we apply the some real datasets collected from Saudi Arabia with the corresponding explanatory variables to the theoretical findings. The Bayesian approach shows better performance compare to the classical approach in terms of the considered performance criteria.

Arthropods in Cosmetics, Pharmaceuticals and Medicine: A Review

“…Cantharidin is a vesicant (blistering agent) produced by beetles belonging to the order of Coleoptera and the family of Meloidae [71]. It is odorless, colorless fatty acid of the terpenoid class secreted by many species of blister beetle, produced by male beetles as defense substance and given to female beetles as a copulatory gift [72,73]. Post-copulation behavior of the female beetle involves the protection of the eggs against any potential predators by covering it with cantharidin.…”

“…Cantharidin has been available synthetically since the 1950s, topical applications of cantharidin have been used predominantly as a treatment for cutaneous warts [72,73]. In 1962 however, marketers of cantharidin failed to produce sufficient efficacy data, resulting in the FDA revision of approval of cantharidin.…”