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Shannon entropy; power law; word frequency distribution; vocabulary quotient; Kullback–Leibler divergence

A statistical study has been conducted on Bhagavad Gita. Four measures have been derived for the original text in Sanskrit and its translations in Hindi, English and French. First, word frequency distributions for the documents were modelled. Power law was observed with the longest tail in the case of Sanskrit. For other versions, the distributions well replicated the Zipf–Mandelbrot pattern. Second, the Kullback–Leibler (KL) divergence betweenthe documents has been computed with the highest value recorded in all three translations from the Sanskrit text. Next, a Shannon entropy-based measure: vocabulary quotient has been calculated, which estimates the vocabulary richness the texts offer; the highest being in the case of Bhagavad Gita in Sanskrit. Finally, word-length distributions were obtained with the longest word length in Sanskrit. The results attribute to the inflectional nature of Sanskrit.

NIKHIL KUMAR RAJPUT¹ BHAVYA AHUJA¹ MANOJ KUMAR RIYAL²

1. Department of Computer Science, Ramanujan College, University of Delhi, New Delhi 110 019, India
2. Department of Physics, Veer Chandra Singh Garhwali Uttarakhand University of Horticulture and Forestry, Tehri Garhwal 246 123, India

Published

1 April 2019

Manuscript received

2 July 2018

Manuscript revised

8 August 2018

Accepted

27 August 2018

Early published

Unedited version published online

Final version published online

15 February 2019