The paper presents introduction to gamma function G(k), generalization and extension of the gamma function. Further generalization of the extended gamma function with five parameters is proposed, and their applications in different fields are presented. This new generalized function open possibilities to represent mixture random phenomena in distribution theory. The extension of gamma function opens a new direction of research for statistical quality control.
Mathematics Subject Classification: 62P99
Keywords: Special function; Gamma function; Beta function; Generalized; Extended; Distribution theory