Statistics is the science whereby inferences are made about specific random phenomena on the basis of relatively limited sample material. The field of statistics can be subdivided into two main areas: mathematical statistics and applied statistics. Mathematical statistics concerns the development of new methods of statistical inference and requires detailed knowledge of basic mathematics for its implementation. Applied statistics concerns the application of the methods of mathematical statistics to specific subject areas such as economics, psychology and public health. Biostatistics is a branch of applied statistics that concerns the application of statistical methods to medical and biological problems. Nowadays much concern is devoted to hospital utility statistics, audit, resource allocation, vaccination uptake, incidence and prevalence of different diseases, assessment of drugs and medical diagnostic tests. Bio-statistical methods help us to analyze the obtained data from different researches, such as clinical trials, systematic reviews, genetic and proteomics surveys, and epidemiologic studies.

Background & Aim: Due to the applicability of the statistical distributions in many areas of sciences, adding parameters to an existing distribution for developing more flexible models have been overlooked in the statistical literatures. Methods & Materials: A new generalization of power distribution is proposed using alpha power transformation method. The new distribution is more flexible than the power distribution and contains distributions that can be unimodal or right skewed. Results: We study some statistical properties of the new distribution, including mean residual lifetime, quantiles, mode, moments, moment generating function, order statistics, some entropies and maximum likelihood estimators. Conclusion: We fit the APP and some competitive models to one real data set and show that the new model has a superior performance among the compared distributions as evidenced by some goodness-of fit statistics.