Weibull distributions were fitted to wind speed data from radiosonde stations in the global tropics. A statistical theory of equatorial waves was proposed to explain the shape parameter k obtained over Malay Peninsula and the wider Equatorial Monsoon Zone. The theory uses the (−5/3)-power law in quasi-2-D turbulence, classical Boltzmann statistics and the Central Limit Theorem. It provides a statistical dynamical basis for using empirical Weibull fits to derive wind speed thresholds for monitoring data quality. The regionally adapted thresholds retain more useful data than conventional ones defined from taking the regional mean plus three standard deviations. The new approach is shown to eliminate reports of atypically strong wind over Malay Peninsula which may have escaped detection in quality control of global datasets as the latter has assumed a larger spread of wind speed.