A new extended distribution and its application to using survival analysis of cancer patients

Medical research is one of the most important aspects of statistical analysis and application. In this paper, present a new three-parameter continuous distribution referred to as power exponentiated Shanker distributions with application to real-life datasets. The proposed distri-bution possesses a density function, a distribution function with three parameters, a survival function, and a hazard function. They studied the nature of the distribution with the help of its statistical properties, including moments, moment-generating functions, and entropy. The probability density function of order statistics for this distribution is also obtained. The classical distribution is the estimation of parameters by using the technique of maximum likelihood estimation. The application of the model selection technique criteria AIC, BIC, AICC, and goodness of fit on two real data sets is finally presented and compared to the fit attained by some other well-known distributions.