Nairobi Securities Exchange 20 Index Share (NSE-20 Share Index/ An Exchange Traded Fund) has been one of
the investment avenues for both Kenyans and foreign investors look whenever they want to make sound
investments decisions in the market. However, the assumption that the daily securities index prices follows a
normal distribution has been disputed by data in several cases. This means new statistical distributions must be
used to discern the distribution of NSE-20 Share Index thus enabling investors make prudent financial decisions
to avoid financial loses. In this research paper, we will model the prices of daily securities index using a log-normal
distribution. This is because the distribution follows a positive trend before we can ascertain on how well it fits
the already available data at the NSE market. This research paper recommends that a log-normal distribution best
fits data of the daily prices of NSE-20 Share Index for those investors who would like to model the future of the
market before making financial decisions.