A statistical probe into the word frequency and length distributions prevalent in the translations of Bhagavad Gita

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 between the 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.