Modification of Price Performance Analytics: A Beta-G Family of Distributions
Abstract
Modification of the pro-forma of wholesale price performance of commodities has received less attention due to its technicality, mathematical derivations, rigorous computations and bounded observations. This study examined nine (9) robust members of the Beta-G family of distributions for the modification of the price performance analytics of Value-at-Risk indexes - Sharpe Ratio, Multi-period & Annualized variations, and Tracking Error indexes.
The retail prices of cereals in Kano state, Nigeria were the empirical data used to verify derived solutions via tangent method for root finding. Log-logistic distributional noise for the prices of rice, maize, sorghum millet, guinea corn, cowpea, groundnut, beans, wheat and cassava produced the minimum positive risk-free rate unit of volatility of 1.6518, 0.5674, 11.3893, 9.2828, 8.8755, 10.1269, 4.1438, 41.8871, and 7.1491 respectively. Chen random noise absolved the characterized fluctuations/noisy traits in the prices of the cereals to give minimum annual and quarterly coefficient of variations of (0.8909 & 0.445); (0.8327 & 0.4163742); (0.7852 & 0.3926); (0.7819 & 0.3909); (0.8812 & 0.4406); (0.81163 & 0.4058); (0.8281 & 0.4141); (0.7873 & 0.3937); and (7.1491 & 0.8538) for maize, sorghum, millet, guinea corn, cowpea, groundnut, beans, wheat, and cassava respectively.
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