Noting that frequency distributions of clearness indices available in the literature are not applicable for all climates, the present article examines the suitability of a new parameter,(K) over cap (T), and a variable, (A) over cap (T) to depict generalized clearness index distributions. K, is a normalized monthly average daily clearness index, while (K) over cap (T),is a normalized daily clearness index. These normalized clearness indices comprise maximum and minimum daily clearness indices (K-T,(max) and K-T,(min)), in a month, in addition to monthly average daily clearness index, (K) over bar (T), and daily clearness index, K-T. Correlations have been developed to predict K-T,K-max and K-T,K-min needed, in the absence of data. The distributions, developed in terms of (K) over cap (T) and (K) over cap (T) have been suitably represented and tested over 70 locations, latitudes ranging from 8 degreesN to 64 degreesN. The daily clearness index values have been predicted within a standard deviation of 0.034 with the expressions developed in the present study. (C) 2001 Elsevier Science Ltd. All rights reserved.