The gamma distribution is one of the continuous distributions. Gamma distributions are very versatile and give useful presentations of many physical situations. They are perhaps the most applied statistical distribution in the area of reliability. Gamma distributions are of different types, 1, 2, 3, 4-parameters. They are applied in different fields, among them finance, economics, hydrological and in civil engineering. In this study we have constructed different types of gamma distributions using transformation/change of variable and cumulative techniques and calculated their properties using moments, identified their special cases and calculated their properties too. We have also constructed gamma related distribution using transformation and cumulative techniques and most of these distributions are expressed using special functions, also we have used the gamma-generator and gamma exponetiated-generator to generate new family of distributions.

Ayienda K. Carolynne studied at the University of Nairobi obtaining a Bachelor of Science degree in Mathematics (Statistics Major) in 2006. In 2011 she obtained a full University of Nairobi scholarship to study a masters of Science degree in Statistics. She graduated with a Master of Science degree in Statistics in 2013 from the same University. Her masters project was on gamma and related distribution with an aim of constructing new distributions. Currently, she is a drought information officer with the National Drought Management Authority, Kenya.