Actuarial science is based on the use of financial and statistical models and depends on the practical framework, starting from the operation of the insurance market through the accounting system and the available data. Actuarial profession is highly valued in the world, due to the possibilities of significant financial benefits, but also because of the increasing expansion of the profession in different spheres of business. In order to perform his/her job successfully, an actuary needs to possess certain knowledge of statistics and mathematics to adequately evaluate the risk. Risk evaluation is a complex and responsible job, which requires from an actuary to know how to apply the statistical theory of credibility and its main methods. This paper presents some of the initial methods on which today’s methodologies in actuarial science are based and developed.