A Multivariate Weibull Disitribution

TL;DR

This paper develops a multivariate Weibull distribution model, deriving its key functions and applying it to tumor data in female rats to demonstrate its practical utility.

Contribution

It extends the Weibull distribution to a multivariate context by expanding previous theorems and derives comprehensive functions for this new model.

Findings

Derived the multivariate survival and density functions.

Applied the model to tumor data in female rats.

Demonstrated the model's applicability to real-world data.

Abstract

A multivariate survival function of Weibull Distribution is developed by expanding the theorem by Lu and Bhattacharyya (1990). From the survival function, the probability density function, the cumulative probability function, the determinant of the Jacobian Matrix, and the general moment are derived. The proposed model is also applied to the tumor appearance data of female rats.