#### Abstract

In the most of all statistical approaches in pattern recognition theories in remote sensing it is assumed that each probability density function of pattern classes can be approximated by the Gaussian probability density function. However, this assumption is not always appropriate in practice. The exact shape of class probability density function is supposed to be expressed as an original histogram. And if the shape of the histogram is largely different from the Gaussian function the classification results might include large error.

Therefore, there seems no need to persist in Gaussian probability density function as the only representation of class histograms. In other words, if there are other functions which can approximate the original histograms more accurately than the Gaussian function can, we would better to adopt one of those functions as a representation of a pattern class histogram.

From this point of view, a probability density function was expanded by adding another parameter to the Gaussian function so that it can approximate histograms more flexibly and still can include the Gaussian function itself as a special case.

The expanded function used here is a non-symmetric Gaussian function which has two independent standard deviations for each Side of the mode so that it can approximate the anti-symmetricity of class histogram.

In this paper some characteristics of the non-symmetric Gaussian probability density function were studied. Then the fitness to the original histogram was examined by chi-square test and compared with that of the conventional symmetric Gaussian function. The comparison between symmetric and non-symmetric function was accomplished also on the results of a test run.

#### Date of this Version

1981