In this study, the proportions of electricity consumption of Turkey in 2006 with respect of some sectors are estimated by using Kullback's Minimum Cross-Entropy (MinxEnt) Principle. In order to realize mentioned estimation the required constraint value is forecasted by ARIMA (Auto-Regressive Integrated Moving Average) which is one of the most important time series analyses. Firstly a data set consists of quantities and values of total electricity consumption of Turkey in 1996-2005 are used for forecasting this constraint. Then an arranged data set formed by unit prices and proportions of electricity consumption according to the sectors in 2005 is used to solve the estimation problem by MinxEnt Principle. The mentioned estimation problem is transformed to a functional equation by Lagrange's multipliers method and solved by Newton's Method. A Visual Basic program is written for the whole estimating process.