Abstract: In this paper we discussed new Lindley Distribution for nocturnal gherlin pulsatility and response to growth hormone. The physiological importance of endogenous ghrelin as a potential participant in the regulation of GH secretion is still unknown. In this study, the author investigated ghrelin pulsatility compared with GH during overnight fasting and eight healthy male subjects to determine ghrelin pulsatility, pattern of coupling, synchronicity to GH, and response to standard GH secretagogues, including GH releasing hormone(GHRH) aloneandin combination with arginine. Using mathematical model by the author investigated whether fluctuations in plasma ghrelin concentrations during overnight fasting exhibited pattern coupling and synchronicity to GH by use of cross-approximate entropy (X-ApEn). We analyzed ghrelin and GH concentration during overnight fasting when ghrelin and GH peak.