A modified box and cox power transformation to determine the standardized precipitation index

Abstract

© 2018, Prince of Songkla University. All rights reserved. The objective of this research was to create a new transformation method, based on a modification of the Box and Cox power transformation (SMBC) by adding the ratio of skewness to two sample sizes, to characterized rought conditions with a standardized precipitation index (SPI). Along with the various classical data transformations, namely the Box and Cox power transformation (BC), the exponential transformation, the Yeo and Johnson transformation, and a modification to BC by adding range, the results of a simulation study showed that the BC and SMBC methods had similar efficiencies when transforming gamma data, Weibull data, and Pearson type III data to a normal distribution, and notably, SMBC performed particularly well with the latter. Drought conditions were evaluated using the SMBC transformation on real-life data from rain gauging stations at Muang (Lamphun), Mae Prik (Lampang) and Chom Thong (Chiang Mai), Thailand. The SMBC proved to be particularly useful in determining the SPI.