A Mathematical Model for the Genetic Variation of Prolactin and Prolactin Receptor in Relationship with Serum Prolactin Concentrations and Breast Cancer Risk

摘要

The Weibull distribution is a widely used model for studying fatigue and endurance life in engineering devices and materials. Recent advances in Weibull theory have also created numerous specialized Weibull applications. Modern computing technology has made many of these techniques accessible across the engineering spectrum. Despite its popularity, and wide applicability the traditional 2 – parameter and 3- parameter Weibull distribution is unable to capture all the lifetime phenomenon for instance the data set which has a non – monotonic failure rate function. Recently several generalization of Weibull distribution has been studied. An approach to the construction of flexible parametric model is to embed appropriate competing models into a larger model by adding shape parameter. Some recent generalizations of Weibull distribution including the Exponentiated Weibull, Extended Weibull, Modified Weibull are discussed and references [5] therein, along with their reliability functions. In this paper a new generalization of Weibull distribution called the transmuted Weibull distribution is utilized for our medical application. For example, Prolactin and prolactin receptors are present in normal breast tissue, benign breast disease, breast cancer cell lines, and breast tumour tissue, leading to speculation that the proliferative and antiapoptotic effects of prolactin in breast epithelial cells could be a factor in breast carcinogenesis. In this paper, a test for the distribution of prolactin concentrations in controls, by menopausal status and relationships with Serum Prolactin Levels and Breast Cancer Risk was investigated in the application part, by using Transmuted Weibull Distribution. As a result the mathematical curves for the Probability Density Function, Reliability Function and Hazard Rate Function are obtained for the corresponding medical curve given in the application part.