The Activity Index (AI) is a well-known index for comparing the contribution of different entities on various fields, for example scientific articles with authorships from different countries structured into various subjects as arts, engineering, economics and so on. This index lacks important properties; the most demonstrative one is its characteristic to be lower but not upper bounded. Further, we will show that the AI is a log-normal distribution and that it is common in literature to transform the AI by the logarithm to a normal distribution. Last, we will present an alternative transformation special for longitudinal data, that transforms the AI to a normal distribution, too, without the negative properties of the logarithm like the loss of data if the logarithm is applied. This newly introduced index called Normalized AI (NAI) will be calculated by expansion the relation of the AI in dividend as in divisor. It will not converge to the logarithm of the AI, but to the logarithm of the AI if z-standardized by each entity-field combination.