Theoretical analysis demonstrates enhanced flexibility in the Gull Alpha Power transform Weibull distribution, highlighting utility for modeling cancer and engineering data.
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 .
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Aljumaily et al. (2024) studied this question.
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