Study of Alpha Power Weibull Distribution with Application

Abstract

     The Gull Alpha power transform (GAPT) is a family which introduces a single additional parameter to classical continuous probability distribution.The parameter increases the flexibility of classical distribution. This  family is used to make the standard Weibull distribution which is called a Gull Alpha Power transform  Weibull (GAPTW) distribution more flexible in application  .Some statistical properties of GAPTW distribution , median ,quartiles ,moments and mode have been discussed. Maximum Product of Spacing (MPS) and Cramer _Von Mises (CVM) method of estimation is used to estimate the parameters of the distribution .It is concluded that the GAPTW is a heavier tailed than weibull distribution and its (hr) function can be increasing,  decreasing or bathtube when the shape parameters is defined  on sub intervals of their sample space. From the application side, the GAPTW  distribution has a flexible application in medical field , specifically  in modeling cancer data and an  engineering field .   

Keywords

• gull alpha power transform
• maximum product spacing (mps) method
• crammer _von mises (cvm) method
• weibull distribution