On achieving near-optimal “Anti-Bayesian” Order Statistics-Based classification fora asymmetric exponential distributions

This paper considers the use of Order Statistics (OS) in the theory of Pattern Recognition (PR). The pioneering work on using OS for classification was presented in [1] for the Uniform distribution, where it was shown that optimal PR can be achieved in a counter-intuitive manner, diametrically opposed to the Bayesian paradigm, i.e., by comparing the testing sample to a few samples distant from the mean - which is distinct from the optimal Bayesian paradigm. In [2], we showed that the results could be extended for a few symmetric distributions within the exponential family. In this paper, we attempt to extend these results significantly by considering asymmetric distributions within the exponential family, for some of which even the closed form expressions of the cumulative distribution functions are not available. These distributions include the Rayleigh, Gamma and certain Beta distributions. As in [1] and [2], the new scheme, referred to as Classification by Moments of Order Statistics (CMOS), attains an accuracy very close to the optimal Bayes’ bound, as has been shown both theoretically and by rigorous experimental testing

Cloud cover effect of clear-sky index distributions and differences between human and automatic cloud observations

The statistics of clear-sky index can be used to determine solar irradiance when the theoretical clear sky irradiance and the cloud cover are known. In this paper, observations of hourly clear-sky index for the years of 2010--2013 at 63 locations in the UK are analysed for over 1 million data hours. The aggregated distribution of clear-sky index is bimodal, with strong contributions from mostly-cloudy and mostly-clear hours, as well as a lower number of intermediate hours. The clear-sky index exhibits a distribution of values for each cloud cover bin, measured in eighths of the sky covered (oktas), and also depends on solar elevation angle. Cloud cover is measured either by a human observer or automatically with a cloud ceilometer. Irradiation (time-integrated irradiance) values corresponding to human observations of "cloudless" skies (0 oktas) tend to agree better with theoretical clear-sky values, which are calculated with a radiative transfer model, than irradiation values corresponding to automated observations of 0 oktas. It is apparent that the cloud ceilometers incorrectly categorise more non-cloudless hours as cloudless than human observers do. This leads to notable differences in the distributions of clear-sky index for each okta class, and between human and automated observations. Two probability density functions---the Burr (type III) for mostly-clear situations, and generalised gamma for mostly-cloudy situations---are suggested as analytical fits for each cloud coverage, observation type, and solar elevation angle bin. For human observations of overcast skies (8 oktas) where solar elevation angle exceeds 10°, there is no significant difference between the observed clear-sky indices and the generalised gamma distribution fits

On simulating non-normal distributions

simulation, computer methods,

The lognormal approximation to the lead time demand in inventory control

This paper is intended to show that the lognormal distribution can be used to approximate the lead time demand in inventory control problems. The computations involved with this approximation are shown to be simpler compared to the gamma distribution approximation. Some pertinent properties of the lognormal distribution are summarized. Numerical examples are given in two cases of distributed demands and lead times and in each case the lognormal approximation results are compared with the exact and/or other approximations.