A Fuzzy Mathematical Model for the Parathyroid Hormone Secretion in Health Using LOG Gamma Distribution

Abstract

In this paper, the formula for mean and variance of fuzzy log gamma distribution was developed and is used to find the dynamics of parathyroid hormone secretion in health and secondary hyperparathyroidism.
Introduction: Mathematical modeling Problems in engineering, computational science and the physical and biological sciences are using gradually more complicated mathematical techniques. PTH secretion is forbidden by the serum calcium concentration, it is also significant to recognize that during its calcemic actions, PTH regulates the serum calcium concentration. The rate of calcium reduces affect the maximal PTH response to hypocalcaemia has been a topic of concentration.  
Methods: Probability theory and statistics, the comprehensive multivariate log-gamma (G-MVLG) distribution is a multivariate distribution introduced by Demirhan and Hamurkaroglu in 2011. The G-MVLG is an elastic distribution.  This enables one to manage dispersion of the distribution.
Results: The result shows that the fuzzy mean increases in lower alpha cuts and decreases in upper alpha cuts and also the fuzzy variance are increases in lower alpha cuts and decreases in upper alpha cuts for the effect of the linear and episodic induction in serum calcium produced higher PTH values.
Conclusions: We exhibit the assessment of dynamics of parathyroid hormones secretion in health and secondary hyperparathyroidism by the guesstimate of expectation and variance with binary parameter Log- Gamma distribution.